Influence maximization under limited network information: Seeding high-degree neighbors

The diffusion of information, norms, and practices across a social network can be initiated by compelling a small number of seed individuals to adopt first. Strategies proposed in previous work either assume full network information or a large degree of control over what information is collected. However, privacy settings on the Internet and high non-response in surveys often severely limit available connectivity information. Here we propose a seeding strategy for scenarios with limited network information: Only the degrees and connections of some random nodes are known. This new strategy is a modification of ‘random neighbor sampling’ (or ‘one-hop’) and seeds the highest-degree neighbors of randomly selected nodes. Simulating a fractional threshold model, we find that this new strategy excels in networks with heavy tailed degree distributions such as scale-free networks and large online social networks. It outperforms the conventional one-hop strategy even though the latter can seed 50% more nodes, and other seeding possibilities including pure high-degree seeding and clustered seeding

Exact Solution of the Klein-Gordon Equation for the PT-Symmetric Generalized Woods-Saxon Potential by the Nikiforov-Uvarov Method

The one-dimensional Klein-Gordon (KG) equation has been solved for the PT-symmetric generalized Woods-Saxon (WS) potential. The Nikiforov-Uvarov(NU} method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have also investigated the positive and negative exact bound states of the s-states for different types of complex generalized WS potentials.Comment: 29 pages, 8 figure

A Next Step in Disruption Management: Combining Operations Research and Complexity Science

Railway systems occasionally get into a state of out-of-control, meaning that there is barely any train is running, even though the required resources (infrastructure, rolling stock and crew) are available. These situations can either be caused by large disruptions or unexpected propagation and accumulation of delays. Because of the large number of aected resources and the absence of detailed, timely and accurate information, currently existing methods cannot be applied in out-of-control situations. Most of the contemporary approaches assume that there is only one single disruption with a known duration, that all information about the resources is available, and that all stakeholders in the operations act as expected. Another limitation is the lack of knowledge about why and how disruptions accumulate and whether this process can be predicted. To tackle these problems, we develop a multidisciplinary framework aiming at reducing the impact of these situations and - if possible - avoiding them. The key elements of this framework are (i) the generation of early warning signals for out-of-control situations using tools from complexity science and (ii) a set of rescheduling measures robust against the features of out-of-control situations, using tools from operations research

A next step in disruption management: combining operations research and complexity science

Railway systems occasionally get into a state of being out-of-control, meaning that barely any train is running, even though the required resources (infrastructure, rolling stock and crew) are available. Because of the large number of affected resources and the absence of detailed, timely and accurate information, currently existing disruption management techniques cannot be applied in out-of-control situations. Most of the contemporary approaches assume that there is only one single disruption with a known duration, that all information about the resources is available, and that all stakeholders in the operations act as expected. Another limitation is the lack of knowledge about why and how disruptions accumulate and whether this process can be predicted. To tackle these problems, we develop a multidisciplinary framework combining techniques from complexity science and operations research, aiming at reducing the impact of these situations and—if possible—avoiding them. The key elements of this framework are (i) the generation of early warning signals for out-of-control situations, (ii) isolating a specific region such that delay stops propagating, and (iii) the app

Structural dynamics of polycrystalline graphene

The exceptional properties of the two-dimensional material graphene make it attractive for multiple functional applications, whose large-area samples are typically polycrystalline. Here, we study the mechanical properties of graphene in computer simulations and connect these to the experimentally relevant mechanical properties. In particular, we study the fluctuations in the lateral dimensions of the periodic simulation cell. We show that over short timescales, both the area A and the aspect ratio B of the rectangular periodic box show diffusive behavior under zero external field during dynamical evolution, with diffusion coefficients DA and DB that are related to each other. At longer times, fluctuations in A are bounded, while those in B are not. This makes the direct determination of DB much more accurate, from which DA can then be derived indirectly. We then show that the dynamic behavior of polycrystalline graphene under external forces can also be derived from DA and DB via the Nernst-Einstein relation. Additionally, we study how the diffusion coefficients depend on structural properties of the polycrystalline graphene, in particular, the density of defects

One-parametric bifurcation analysis of data-driven car-following models

In this study, an equation-free method is used to perform bifurcation analyses of various artificial neural network (ANN) based car-following models. The ANN models were trained on Multiple Car Following (MCF) model output data (ANN-m) and field data (ANN-r). The ANN-m model could capture the behaviour of the MCF model in quite detail. A bifurcation analysis, using the circuit length L as parameter, for the ANN-m model leads to good results if the training data set from the MCF model is sufficiently diverse, namely that it incorporates data from a wide range of vehicle densities that encompass the stable free-flow and the stable jam-flow regimes. The ANN-r model is in general able to capture the feature of traffic jams when a car takes headway and velocity of itself and of the two cars ahead as input. However, the traffic flow of the ANN-r model is more regular in comparison to the field data. It is possible to construct a partial bifurcation diagram in L for the ANN-r using the equation-free method and it is found that the flow changes stability due to a subcritical Hopf bifurcation

Hidden dependence of spreading vulnerability on topological complexity

Many dynamical phenomena in complex systems concern spreading that plays out on top of networks with changing architecture over time—commonly known as temporal networks. A complex system's proneness to facilitate spreading phenomena, which we abbreviate as its “spreading vulnerability,” is often surmised to be related to the topology of the temporal network featured by the system. Yet, cleanly extracting spreading vulnerability of a complex system directly from the topological information of the temporal network remains a challenge. Here, using data from a diverse set of real-world complex systems, we develop the “entropy of temporal entanglement” as a quantity to measure topological complexities of temporal networks. We show that this parameter-free quantity naturally allows for topological comparisons across vastly different complex systems. Importantly, by simulating three different types of stochastic dynamical processes playing out on top of temporal networks, we demonstrate that the entropy of temporal entanglement serves as a quantitative embodiment of the systems' spreading vulnerability, irrespective of the details of the processes. In being able to do so, i.e., in being able to quantitatively extract a complex system's proneness to facilitate spreading phenomena from topology, this entropic measure opens itself for applications in a wide variety of natural, social, biological, and engineered systems

Complex Interactions with the Surroundings Dictate a Tagged Chain's Dynamics in Unentangled Polymer Melts

For more than half a century the theoretical landscape for single chain dynamics for dense polymeric solutions and melts below the entanglement threshold has been dominated by the Rouse model for independent phantom chains, supported by ideas of hydrodynamic screening. There exists, however, a large body of literature from experiments, Monte Carlo, and molecular dynamics simulations on the deviations from the Rouse behavior for unentangled homopolymer melts, showcased mostly in the subdiffusive behavior of center-of-mass of tagged chains at intermediate times, with the subdiffusion exponent reported in the range 0.75-0.85. The influence of the surrounding chains of length Ns on the motion of a single tagged chain of length N is a key test, by which, through high-precision numerical simulation of unentangled melts, we show that the Rouse model fails. Our central results are that at intermediate times the tagged chains center-of-mass moves subdiffusively, proportional to t(alpha) with subdiffusion exponent alpha = 0.87 +/- 0.03 as opposed to alpha(Rouse) = 1, and that its crossover time to Fickian behavior is directly controlled by the relaxation time of the surrounding chains when the latter are shorter. The terminal relaxation time for the tagged chain and the long time diffusion coefficient are then sensitive to N-s. Both measured exponent flow, that is plots of d alpha(t)/d ln (t) vs alpha(t) where alpha(t) is the effective exponent between and t, and successful blob scaling arguments support the anomalous value of alpha as a true exponent. We find the same exponent in the scaling of Rouse mode amplitude correlation functions and directly related exponent for the monomeric diffusion. We show that the consequences of these results on the dynamics of a tagged monomer and the chains segmental orientation autocorrelation function agree very well with rheological measurements and NMR relaxometry experiments. We reflect back on a history of related experimental anomalies and discuss how a new theory might be developed

Characterizing neural phase-space trajectories via Principal Louvain Clustering

Background With the growing size and richness of neuroscience datasets in terms of dimension, volume, and resolution, identifying spatiotemporal patterns in those datasets is increasingly important. Multivariate dimension-reduction methods are particularly adept at addressing these challenges. New method In this paper, we propose a novel method, which we refer to as Principal Louvain Clustering (PLC), to identify clusters in a low-dimensional data subspace, based on time-varying trajectories of spectral dynamics across multisite local field potential (LFP) recordings in awake behaving mice. Data were recorded from prefrontal cortex, hippocampus, and parietal cortex in eleven mice while they explored novel and familiar environments. Results PLC-identified subspaces and clusters showed high consistency across animals, and were modulated by the animals’ ongoing behavior. Conclusions PLC adds to an important growing literature on methods for characterizing dynamics in high-dimensional datasets, using a smaller number of parameters. The method is also applicable to other kinds of datasets, such as EEG or MEG