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In this paper we presented a novel constructive approach for training deep neural networks using geometric approaches. We show that a topological covering can be used to define a class of distributed linear matrix inequalities, which in…

The hitting set problem is a well-known NP-hard optimization problem in which, given a set of elements and a collection of subsets, the goal is to find the smallest selection of elements, such that each subset contains at least one element…

Controlling a complex network is of great importance in many applications. The network can be controlled by inputting external control signals through some selected nodes, which are called input nodes. Previous works found that the majority…

Although Shapley additive explanations (SHAP) can be computed in polynomial time for simple models like decision trees, they unfortunately become NP-hard to compute for more expressive black-box models like neural networks - where…

Shortest paths in complex networks play key roles in many applications. Examples include routing packets in a computer network, routing traffic on a transportation network, and inferring semantic distances between concepts on the World Wide…

For a network formed by nodes and undirected links between pairs of nodes, the network optimal attack problem aims at deleting a minimum number of target nodes to break the network down into many small components. This problem is…

Diverse higher-order structures, foundational for supporting a network's "meta-functions", play a vital role in structure, functionality, and the emergence of complex dynamics. Nevertheless, the problem of dismantling them has been…

In this paper, we consider a population of individuals who have actions and opinions, which coevolve, mutually influencing one another on a complex network structure. In particular, we formulate a control problem for this social network, in…

This paper proposes network recasting as a general method for network architecture transformation. The primary goal of this method is to accelerate the inference process through the transformation, but there can be many other practical…

We present a method for the reconstruction of networks, based on the order of nodes visited by a stochastic branching process. Our algorithm reconstructs a network of minimal size that ensures consistency with the data. Crucially, we show…

Networked representations of real-world phenomena are often partially observed, which lead to incomplete networks. Analysis of such incomplete networks can lead to skewed results. We examine the following problem: given an incomplete…

Can we employ one neural model to efficiently dismantle many complex yet unique networks? This article provides an affirmative answer. Diverse real-world systems can be abstracted as complex networks each consisting of many functional nodes…

This work presents a neural network that consists of nodes with heterogeneous sensitivity. Each node in a network is assigned a variable that determines the sensitivity with which it learns to perform a given task. The network is trained by…

In this paper, we develop the themes presented at the 2003 Joint Complexity Conference at the London School of Economics and subsequently published in The Intelligencer (2004) and O Tempo Das Redes (2008). Following the data analysis of the…

We consider a strategic network monitoring problem involving the operator of a networked system and an attacker. The operator aims to randomize the placement of multiple protected sensors to monitor and protect components that are…

When nodes can repeatedly update their behavior (as in agent-based models from computational social science or repeated-game play settings) the problem of optimal network seeding becomes very complex. For a popular spreading-phenomena model…

In this paper, we study a model reduction technique for leader-follower networked multi-agent systems defined on weighted, undirected graphs with arbitrary linear multivariable agent dynamics. In the network graph of this network, nodes…

Efficient marketing or awareness-raising campaigns seek to recruit $n$ influential individuals -- where $n$ is the campaign budget -- that are able to cover a large target audience through their social connections. So far most of the…

Concomitant with the tremendous prevalence of online social media platforms, the interactions among individuals are unprecedentedly enhanced. People are free to interact with acquaintances, express and exchange their own opinions through…

This work provides an architecture to enable robotic grasp planning via shape completion. Shape completion is accomplished through the use of a 3D convolutional neural network (CNN). The network is trained on our own new open source dataset…