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   L. Ruiz, L. F. (December 2020, 34th Conference on Neural Information Processing Systems)
2. The duality of networks and groups: Models to generate two-mode networks from one-mode networks

   https://doi.org/10.1017/nws.2023.3  

   Neal, Zachary P. (January 2023, Network Science)

   Abstract Shared memberships, social statuses, beliefs, and places can facilitate the formation of social ties. Two-mode projections provide a method for transforming two-mode data on individuals’ memberships in such groups into a one-mode network of their possible social ties. In this paper, I explore the opposite process: how social ties can facilitate the formation of groups, and how a two-mode network can be generated from a one-mode network. Drawing on theories of team formation, club joining, and organization recruitment, I propose three models that describe how such groups might emerge from the relationships in a social network. I show that these models can be used to generate two-mode networks that have characteristics commonly observed in empirical two-mode social networks and that they encode features of the one-mode networks from which they were generated. I conclude by discussing these models’ limitations and future directions for theory and methods concerning group formation. 

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3. The Age of Gossip in Networks

   https://doi.org/10.1109/ISIT45174.2021.9517796  

   Yates, Roy D. (July 2021, 2021 IEEE International Symposium on Information Theory (ISIT))

   A source node updates its status as a point process and also forwards its updates to a network of observer nodes. Within the network of observers, these updates are forwarded as point processes from node to node. Each node wishes its knowledge of the source to be as timely as possible. In this network, timeliness is measured by a discrete form of age of information: each status change at the source is referred to as a version and the age at a node is how many versions out of date is its most recent update from the source. This work introduces a method for evaluating the average version age at each node in the network when nodes forward updates using a memoryless gossip protocol. This method is then demonstrated by version age analysis for a collection of simple networks. For gossip on a complete graph with symmetric updating rates, it is shown that each node has average age that grows as the logarithm of the network size. 

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4. The Dynamics of Canalizing Boolean Networks

   https://doi.org/10.1155/2020/3687961  

   Paul, Elijah; Pogudin, Gleb; Qin, William; Laubenbacher, Reinhard (January 2020, Complexity)

   Boolean networks are a popular modeling framework in computational biology to capture the dynamics of molecular networks, such as gene regulatory networks. It has been observed that many published models of such networks are defined by regulatory rules driving the dynamics that have certain so-called canalizing properties. In this paper, we investigate the dynamics of a random Boolean network with such properties using analytical methods and simulations. From our simulations, we observe that Boolean networks with higher canalizing depth have generally fewer attractors, the attractors are smaller, and the basins are larger, with implications for the stability and robustness of the models. These properties are relevant to many biological applications. Moreover, our results show that, from the standpoint of the attractor structure, high canalizing depth, compared to relatively small positive canalizing depth, has a very modest impact on dynamics. Motivated by these observations, we conduct mathematical study of the attractor structure of a random Boolean network of canalizing depth one (i.e., the smallest positive depth). For every positive integer ℓ , we give an explicit formula for the limit of the expected number of attractors of length ℓ in an n -state random Boolean network as n goes to infinity. 

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5. Neural Networks Optimally Compress the Sawbridge

   https://doi.org/10.1109/DCC50243.2021.00022  

   Wagner, Aaron B.; Balle, Johannes (March 2021, Data Compression Conference)

   null (Ed.)