Related papers: Structure, Scaling and Phase Transition in the Opt…
Transport networks are crucial to the functioning of natural and technological systems. Nature features transport networks that are adaptive over a vast range of parameters, thus providing an impressive level of robustness in supply.…
The length dependence is computed of the resistance of a disordered normal-metal wire attached to a superconductor. The scaling of the transmission eigenvalue distribution with length is obtained exactly in the metallic limit, by a…
The last decade has shown a tremendous success in solving various computer vision problems with the help of deep learning techniques. Lately, many works have demonstrated that learning-based approaches with suitable network architectures…
Networks constructed out of resistors, inductors, capacitors and transformers form a compelling subclass of simple models. Models constructed out of these basic elements are frequently used to explain phenomena in large-scale applications,…
In practical terms, controlling a network requires manipulating a large number of nodes with a comparatively small number of external inputs, a process that is facilitated by paths that broadcast the influence of the (directly-controlled)…
Current dissipation in thin superconducting wires is numerically evaluated by using the string method, within the framework of time-dependent Ginzburg-Landau equation with a Langevin noise term. The most probable transition pathway between…
The coupling constant dependence is derived in time-dependent {\em current} density functional theory. The scaling relation can be used to check approximate functionals and in conjunction with the adiabatic connection formula to obtain the…
In this paper, we reveal the relationship between entropy rate and the congestion in complex network and solve it analytically for special cases. Finding maximizing entropy rate will lead to an improvement of traffic efficiency, we propose…
The optimal power flow (OPF) problem determines power generation/demand that minimize a certain objective such as generation cost or power loss. It is nonconvex. We prove that, for radial networks, after shrinking its feasible set slightly,…
This lecture discusses the mathematical relationship between network structure and network utilization of transportation network. Network structure means the graph itself. Network utilization represent the aggregation of trajectories of…
We perform numerical simulations to study the optimal path problem on disordered hierarchical graphs with effective dimension d=2.32. Therein, edge energies are drawn from a disorder distribution that allows for positive and negative…
We have revealed general physical conditions for the {\it maximization} of the network throughput at which free flow conditions are ensured, i.e., traffic breakdown cannot occur in the whole traffic or transportation network. A physical…
In this Rapid Communication we investigate spatially constrained networks that realize optimal synchronization properties. After arguing that spatial constraints can be imposed by limiting the amount of `wire' available to connect nodes…
The structure and design of optimal supply networks is an important topic in complex networks research. A fundamental trait of natural and man-made networks is the emergence of loops and the trade-off governing their formation: adding…
The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this…
We introduce the notion of a network's conduciveness, a probabilistically interpretable measure of how the network's structure allows it to be conducive to roaming agents, in certain conditions, from one portion of the network to another.…
It is demonstrated that power-laws which are modified by logarithmic corrections arise in supercorrelated systems. Their characteristic feature is the energy attributed to a state (or value of a general cost function) which depends…
In this paper, we present a simple model of scale-free networks that incorporates both preferential & random attachment and anti-preferential & random deletion at each time step. We derive the degree distribution analytically and show that…
Adaptive transport networks in biological and physical systems exhibit hierarchical organization, characteristic channel spacing, and robust scaling relations. Existing adaptive network models, formulated on a lattice, successfully…
We study an optimization problem related to the approximation of given data by a linear combination of transformed modes. In the simplest case, the optimization problem reduces to a minimization problem well-studied in the context of proper…