81,015 research outputs found
Multiple structural transitions in interacting networks
Many real-world systems can be modeled as interconnected multilayer networks,
namely a set of networks interacting with each other. Here we present a
perturbative approach to study the properties of a general class of
interconnected networks as inter-network interactions are established. We
reveal multiple structural transitions for the algebraic connectivity of such
systems, between regimes in which each network layer keeps its independent
identity or drives diffusive processes over the whole system, thus generalizing
previous results reporting a single transition point. Furthermore we show that,
at first order in perturbation theory, the growth of the algebraic connectivity
of each layer depends only on the degree configuration of the interaction
network (projected on the respective Fiedler vector), and not on the actual
interaction topology. Our findings can have important implications in the
design of robust interconnected networked system, particularly in the presence
of network layers whose integrity is more crucial for the functioning of the
entire system. We finally show results of perturbation theory applied to the
adjacency matrix of the interconnected network, which can be useful to
characterize percolation processes on such systems
A Positive Theory of Network Connectivity
This paper develops a positive theory of network connectivity, seeking to explain the micro-foundations of alternative network topologies as the result of self-interested actors. By building roads, landowners hope to increase their parcelsĂ accessibility and economic value. A simulation model is performed on a grid-like land use layer with a downtown in the center, whose structure resembles the early form of many Midwest- ern and Western (US) cities. The topological attributes for the networks are evaluated. This research posits that road networks experience an evolutionary process where a tree-like structure first emerges around the centered parcel before the network pushes outward to the periphery. In addition, road network topology undergoes clear phase changes as the economic values of parcels vary. The results demonstrate that even without a centralized authority, road networks have the property of self-organization and evolution, and, that in the absence of intervention, the tree-like or web-like nature of networks is a result of the underlying economics.road network, land parcel, network evolution, network growth, phase change, centrality measures, degree centrality, closeness centrality, betweenness centrality, network structure, treeness, circuitness, topology
Mathematics and the Internet: A Source of Enormous Confusion and Great Potential
Graph theory models the Internet mathematically, and a number of plausible mathematically intersecting network models for the Internet have been developed and studied. Simultaneously, Internet researchers have developed methodology to use real data to validate, or invalidate, proposed Internet models. The authors look at these parallel developments, particularly as they apply to scale-free network models of the preferential attachment type
A combined measure for quantifying and qualifying the topology preservation of growing self-organizing maps
The Self-OrganizingMap (SOM) is a neural network model that performs an ordered projection of a high dimensional input space in a low-dimensional topological structure. The process in which such mapping is formed is defined by the SOM algorithm, which is a competitive, unsupervised and nonparametric method, since it does not make any assumption about the input data distribution. The feature maps provided by this algorithm have been successfully applied for vector quantization, clustering and high dimensional data visualization processes. However, the initialization of the network topology and the selection of the SOM training parameters are two difficult tasks caused by the unknown distribution of the input signals. A misconfiguration of these parameters can generate a feature map of low-quality, so it is necessary to have some measure of the degree of adaptation of the SOM network to the input data model. The topologypreservation is the most common concept used to implement this measure. Several qualitative and quantitative methods have been proposed for measuring the degree of SOM topologypreservation, particularly using Kohonen's model. In this work, two methods for measuring the topologypreservation of the Growing Cell Structures (GCSs) model are proposed: the topographic function and the topology preserving ma
Topology Control Algorithm considering Antenna Radiation Pattern in Three-Dimensional Wireless Sensor Networks
Topology control is a key issue of wireless sensor network to reduce energy consumption and communication collision. Topology control algorithms in three-dimensional space have been proposed by modifying existing two-dimensional algorithms. These algorithms are based on the theoretical assumption that transmission power is radiated equally to the all directions by using isotropic antenna model. However, isotropic antenna does not exist, which is hypothetical antenna to compare the real antenna performance. In the real network, dipole antenna is applied, and because of the radiation pattern, performance of topology control algorithm is degraded. We proposed local remapping algorithm to solve the problem and applied it to existing topology control algorithms. Simulation results show that our algorithm increases performance of existing algorithms and reduces power consumption
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