相关论文: Optimization in Gradient Networks

The ability to control complex networks is of crucial importance across a wide range of applications in natural and engineering sciences. However, issues of both theoretical and numerical nature introduce fundamental limitations to…

We study hierarchical properties of optimal transportation networks with biological background. The networks are obtained as minimizers of an energy functional which involves a metabolic cost term of a power-law form with exponent…

We propose an optimization approach to design cost-effective electrical power transmission networks. That is, we aim to select both the network structure and the line conductances (line sizes) so as to optimize the trade-off between network…

This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…

Congestion in transport networks is a topic of theoretical interest and practical importance. In this paper we study the flow of vehicles in urban street networks. In particular, we use a cellular automata model to simulate the motion of…

Graph Neural Networks (GNNs) have achieved tremendous success in a variety of real-world applications by relying on the fixed graph data as input. However, the initial input graph might not be optimal in terms of specific downstream tasks,…

Although the analysis of loops is not so much because of the complications, it has already been found that heuristically enhancing loops decreases the variance of degree distributions for improving the robustness of connectivity. While many…

This paper presents a distributed optimization scheme over a network of agents in the presence of cost uncertainties and over switching communication topologies. Inspired by recent advances in distributed convex optimization, we propose a…

Transportation and distribution networks are a class of spatial networks that have been of interest in recent years. These networks are often characterized by the presence of complex structures such as central loops paired with peripheral…

Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…

It seems that in the current age, computers, computation, and data have an increasingly important role to play in scientific research and discovery. This is reflected in part by the rise of machine learning and artificial intelligence,…

For scale-free networks with degrees following a power law with an exponent $\tau\in(2,3)$, the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any…

Complex networks are frequently employed to model physical or virtual complex systems. When certain entities exist across multiple systems simultaneously, unveiling their corresponding relationships across the networks becomes crucial. This…

Many networks are characterized by highly heterogeneous distributions of links, which are called scale-free networks and the degree distributions follow $p(k)\sim ck^{-\alpha}$. We study the robustness of scale-free networks to random…

Previously, transport networks are usually treated as homogeneous networks, that is, every node has the same function, simultaneously providing and requiring resources. However, some real networks, such as power grid and supply chain…

Complex networks of real-world systems are believed to be controlled by common phenomena, producing structures far from regular or random. These include scale-free degree distributions, small-world structure and assortative mixing by…

Although the community structure organization is one of the most important characteristics of real-world networks, the traditional network models fail to reproduce the feature. Therefore, the models are useless as benchmark graphs for…

We study partition of networks into basins of attraction based on a steepest ascent search for the node of highest degree. Each node is associated with, or "attracted" to its neighbor of maximal degree, as long as the degree is increasing.…

We propose a Markov chain simulation method to generate simple connected random graphs with a specified degree sequence and level of clustering. The networks generated by our algorithm are random in all other respects and can thus serve as…

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to…