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1. backbone: An R package to extract network backbones

   https://doi.org/10.1371/journal.pone.0269137  

   Neal, Zachary P. (May 2022, PLOS ONE)

   Cherifi, Hocine (Ed.)

   Networks are useful for representing phenomena in a broad range of domains. Although their ability to represent complexity can be a virtue, it is sometimes useful to focus on a simplified network that contains only the most important edges: the backbone. This paper introduces and demonstrates a substantially expanded version of the backbone package for R, which now provides methods for extracting backbones from weighted networks, weighted bipartite projections, and unweighted networks. For each type of network, fully replicable code is presented first for small toy examples, then for complete empirical examples using transportation, political, and social networks. The paper also demonstrates the implications of several issues of statistical inference that arise in backbone extraction. It concludes by briefly reviewing existing applications of backbone extraction using the backbone package, and future directions for research on network backbone extraction. 

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2. Transferring Robustness for Graph Neural Network Against Poisoning Attacks

   https://doi.org/10.1145/3336191.3371851  

   Tang, Xianfeng; Li, Yandong; Sun, Yiwei; Yao, Huaxiu; Mitra, Prasenjit; Wang, Suhang (January 2020, WSDM '20: Proceedings of the 13th International Conference on Web Search and Data Mining)

   Graph neural networks (GNNs) are widely used in many applications. However, their robustness against adversarial attacks is criticized. Prior studies show that using unnoticeable modifications on graph topology or nodal features can significantly reduce the performances of GNNs. It is very challenging to design robust graph neural networks against poisoning attack and several efforts have been taken. Existing work aims at reducing the negative impact from adversarial edges only with the poisoned graph, which is sub-optimal since they fail to discriminate adversarial edges from normal ones. On the other hand, clean graphs from similar domains as the target poisoned graph are usually available in the real world. By perturbing these clean graphs, we create supervised knowledge to train the ability to detect adversarial edges so that the robustness of GNNs is elevated. However, such potential for clean graphs is neglected by existing work. To this end, we investigate a novel problem of improving the robustness of GNNs against poisoning attacks by exploring clean graphs. Specifically, we propose PA-GNN, which relies on a penalized aggregation mechanism that directly restrict the negative impact of adversarial edges by assigning them lower attention coefficients. To optimize PA-GNN for a poisoned graph, we design a meta-optimization algorithm that trains PA-GNN to penalize perturbations using clean graphs and their adversarial counterparts, and transfers such ability to improve the robustness of PA-GNN on the poisoned graph. Experimental results on four real-world datasets demonstrate the robustness of PA-GNN against poisoning attacks on graphs. 

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3. Root and community inference on the latent growth process of a network

   https://doi.org/10.1093/jrsssb/qkad102  

   Crane, Harry; Xu, Min (September 2023, Journal of the Royal Statistical Society Series B: Statistical Methodology)

   Abstract Many statistical models for networks overlook the fact that most real-world networks are formed through a growth process. To address this, we introduce the Preferential Attachment Plus Erdős–Rényi model, where we let a random network G be the union of a preferential attachment (PA) tree T and additional Erdős–Rényi (ER) random edges. The PA tree captures the underlying growth process of a network where vertices/edges are added sequentially, while the ER component can be regarded as noise. Given only one snapshot of the final network G, we study the problem of constructing confidence sets for the root node of the unobserved growth process; the root node can be patient zero in an infection network or the source of fake news in a social network. We propose inference algorithms based on Gibbs sampling that scales to networks with millions of nodes and provide theoretical analysis showing that the size of the confidence set is small if the noise level of the ER edges is not too large. We also propose variations of the model in which multiple growth processes occur simultaneously, reflecting the growth of multiple communities; we use these models to provide a new approach to community detection. 

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4. Implicit definitions with differential equations for KeYmaera X (System Description)

   Gallicchio, James; Tan, Yong Kiam; Mitsch, Stefan; Platzer, André (August 2022, Automated Reasoning, International Joint Conference, IJCAR 2022)

   Blanchette, Jasmin; Kovacs, Laura; Pattinson, Dirk (Ed.)

   Definition packages in theorem provers provide users with means of defining and organizing concepts of interest. This system description presents a new definition package for the hybrid systems theorem prover KeYmaera X based on differential dynamic logic (dL). The package adds KeYmaera X support for user-defined smooth functions whose graphs can be implicitly characterized by dL formulas. Notably, this makes it possible to implicitly characterize functions, such as the exponential and trigonometric functions, as solutions of differential equations and then prove properties of those functions using dL's differential equation reasoning principles. Trustworthiness of the package is achieved by minimally extending KeYmaera X's soundness-critical kernel with a single axiom scheme that expands function occurrences with their implicit characterization. Users are provided with a high-level interface for defining functions and non-soundness-critical tactics that automate low-level reasoning over implicit characterizations in hybrid system proofs. 

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5. Efficient Large-Scale Multi-Drone Delivery using Transit Networks

   https://doi.org/10.1613/jair.1.12450  

   Choudhury, Shushman; Solovey, Kiril; Kochenderfer, Mykel J.; Pavone, Marco (January 2021, Journal of Artificial Intelligence Research)

   We consider the problem of routing a large fleet of drones to deliver packages simultaneously across broad urban areas. Besides flying directly, drones can use public transit vehicles such as buses and trams as temporary modes of transportation to conserve energy. Adding this capability to our formulation augments effective drone travel range and the space of possible deliveries but also increases problem input size due to the large transit networks. We present a comprehensive algorithmic framework that strives to minimize the maximum time to complete any delivery and addresses the multifaceted computational challenges of our problem through a two-layer approach. First, the upper layer assigns drones to package delivery sequences with an approximately optimal polynomial time allocation algorithm. Then, the lower layer executes the allocation by periodically routing the fleet over the transit network, using efficient, bounded suboptimal multi-agent pathfinding techniques tailored to our setting. We demonstrate the efficiency of our approach on simulations with up to 200 drones, 5000 packages, and transit networks with up to 8000 stops in San Francisco and the Washington DC Metropolitan Area. Our framework computes solutions for most settings within a few seconds on commodity hardware and enables drones to extend their effective range by a factor of nearly four using transit. 

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