Related papers: Control core of undirected complex networks
To design control strategies that predictably manipulate a system's behavior, it is first necessary to understand how the system's structure relates to its response. Many complex systems can be represented as multilayer networks whose…
Epidemics, neural cascades, power failures, and many other phenomena can be described by a diffusion process on a network. To identify the causal origins of a spread, it is often necessary to identify the triggering initial node. Here we…
Complex networks usually exhibit a rich architecture organized over multiple intertwined scales. Information pathways are expected to pervade these scales reflecting structural insights that are not manifest from analyses of the network…
Networks are ubiquitous in various fields, representing systems where nodes and their interconnections constitute their intricate structures. We introduce a network decomposition scheme to reveal multiscale core-periphery structures lurking…
This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of…
In pinning control of complex networks, a tacit believing is that the system dynamics will be better controlled by pinning the large-degree nodes than the small-degree ones. Here, by changing the number of pinned nodes, we find that, when a…
The robust disturbance rejection controller has been the subject of intensive research due to its undeniable importance for automation. Modern control theory tends to use model-based approaches versus model-free approaches, especially when…
The traditional node percolation map of directed networks is reanalyzed in terms of edges. In the percolated phase, edges can mainly organize into five distinct giant connected components, interfaces bridging the communication of nodes in…
Many optimization, inference and learning tasks can be accomplished efficiently by means of decentralized processing algorithms where the network topology (i.e., the graph) plays a critical role in enabling the interactions among…
The coupled problems of selecting control nodes and designing control actions for nonlinear network dynamics are fundamental scientific problems with applications in many diverse fields. These problems are thoroughly studied for linear…
We take a unified view of network coding and decentralized control. Precisely speaking, we consider both as linear time-invariant systems by appropriately restricting channels and coding schemes of network coding to be linear…
Disordered fibrous networks are ubiquitous in nature as major structural components of living cells and tissues. The mechanical stability of networks generally depends on the degree of connectivity: only when the average number of…
We generalize the theory of k-core percolation on complex networks to k-core percolation on multiplex networks, where k=(k_a, k_b, ...). Multiplex networks can be defined as networks with a set of vertices but different types of edges, a,…
An important class of real-world networks have directed edges, and in addition, some rank ordering on the nodes, for instance the "popularity" of users in online social networks. Yet, nearly all research related to explosive percolation has…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
This paper studies the problem of controlling complex networks, that is, the joint problem of selecting a set of control nodes and of designing a control input to steer a network to a target state. For this problem (i) we propose a metric…
The $k$-core decomposition in a graph is a fundamental problem for social network analysis. The problem of $k$-core decomposition is to calculate the core number for every node in a graph. Previous studies mainly focus on $k$-core…
We describe a procedure that allows continuously tuning the average degree $\langle k \rangle$ of uncorrelated networks with power-law degree distribution $p(k)$. Inn order to do this, we modify the low-$k$ region of $p(k)$, while…
We tackle the problem of goal-directed graph construction: given a starting graph, a budget of modifications, and a global objective function, the aim is to find a set of edges whose addition to the graph achieves the maximum improvement in…
We consider the $k$-core decomposition of network models and Internet graphs at the autonomous system (AS) level. The $k$-core analysis allows to characterize networks beyond the degree distribution and uncover structural properties and…