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1. Dynamic Network Connectivity: from monkeys to humans

   https://doi.org/10.3389/fnhum.2024.1353043  

   Arnsten, Amy_F T; Wang, Min; D’Esposito, Mark (February 2024, Frontiers in Human Neuroscience)

   Human brain imaging research using functional MRI (fMRI) has uncovered flexible variations in the functional connectivity between brain regions. While some of this variability likely arises from the pattern of information flow through circuits, it may also be influenced by rapid changes in effective synaptic strength at the molecular level, a phenomenon called Dynamic Network Connectivity (DNC) discovered in non-human primate circuits. These neuromodulatory molecular mechanisms are found in layer III of the macaque dorsolateral prefrontal cortex (dlPFC), the site of the microcircuits shown by Goldman-Rakic to be critical for working memory. This research has shown that the neuromodulators acetylcholine, norepinephrine, and dopamine can rapidly change the strength of synaptic connections in layer III dlPFC by (1) modifying the depolarization state of the post-synaptic density needed for NMDA receptor neurotransmission and (2) altering the open state of nearby potassium channels to rapidly weaken or strengthen synaptic efficacy and the strength of persistent neuronal firing. Many of these actions involve increased cAMP-calcium signaling in dendritic spines, where varying levels can coordinate the arousal state with the cognitive state. The current review examines the hypothesis that some of the dynamic changes in correlative strength between cortical regions observed in human fMRI studies may arise from these molecular underpinnings, as has been seen when pharmacological agents or genetic alterations alter the functional connectivity of the dlPFC consistent with the macaque physiology. These DNC mechanisms provide essential flexibility but may also confer vulnerability to malfunction when dysregulated in cognitive disorders. 

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2. Understanding the Importance of Dynamic Landscape Connectivity

   https://doi.org/10.3390/land9090303  

   Zeller, K.A.; Lewison, R.; Fletcher, R.J.; Tulbure, M.G.; Jennings, M.K. (August 2020, Land)

   null (Ed.)

   Landscape connectivity is increasingly promoted as a conservation tool to combat the negative effects of habitat loss, fragmentation, and climate change. Given its importance as a key conservation strategy, connectivity science is a rapidly growing discipline. However, most landscape connectivity models consider connectivity for only a single snapshot in time, despite the widespread recognition that landscapes and ecological processes are dynamic. In this paper, we discuss the emergence of dynamic connectivity and the importance of including dynamism in connectivity models and assessments. We outline dynamic processes for both structural and functional connectivity at multiple spatiotemporal scales and provide examples of modeling approaches at each of these scales. We highlight the unique challenges that accompany the adoption of dynamic connectivity for conservation management and planning in the context of traditional conservation prioritization approaches. With the increased availability of time series and species movement data, computational capacity, and an expanding number of empirical examples in the literature, incorporating dynamic processes into connectivity models is more feasible than ever. Here, we articulate how dynamism is an intrinsic component of connectivity and integral to the future of connectivity science. 

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3. Towards Scalable and Practical Batch-Dynamic Connectivity

   https://doi.org/10.14778/3712221.3712250  

   De_Man, Quinten; Dhulipala, Laxman; Karczmarz, Adam; Łącki, Jakub; Shun, Julian; Wang, Zhongqi (November 2024, Proceedings of the VLDB Endowment)

   We study the problem of dynamically maintaining the connected components of an undirected graph subject to edge insertions and deletions. We give the first parallel algorithm for the problem that is work-efficient, supports batches of updates, runs in polylogarithmic depth, and uses only linear total space. The existing algorithms for the problem either use super-linear space, do not come with strong theoretical bounds, or are not parallel. On the empirical side, we provide the first implementation of the cluster forest algorithm, the first linear-space and polylogarithmic update time algorithm for dynamic connectivity. Experimentally, we find that our algorithm uses up to 19.7× less space and is up to 6.2× faster than the level-set algorithm of Holm, de Lichten-berg, and Thorup, arguably the most widely-implemented dynamic connectivity algorithm with strong theoretical guarantees. 

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4. Fully Dynamic Exact Edge Connectivity in Sublinear Time

   Goranci, Gramoz; Henzinger, Monika; Nanongkai, Danupon; Saranurak, Thatchaphol; Thorup, Mikkel; Wulff-Nilsen, Christian (January 2023, SIAM)
5. Optimal Offline Dynamic 2, 3-Edge/Vertex Connectivity

   Peng, Richard; Sandlund, Bryce; Sleator, Daniel D (July 2019, Algorithms and Data Structures - 16th International Symposium, WADS 2019, Edmonton, AB, Canada, August 5-7, 2019, Proceedings)

   We give offline algorithms for processing a sequence of 2- and 3-edge and vertex connectivity queries in a fully-dynamic undirected graph. While the current best fully-dynamic online data structures for 3-edge and 3-vertex connectivity require O(n^{2/}3) and O(n) time per update, respectively, our per-operation cost is only O(logn) , optimal due to the dynamic connectivity lower bound of Patrascu and Demaine. Our approach utilizes a divide and conquer scheme that transforms a graph into smaller equivalents that preserve connectivity information. This construction of equivalents is closely-related to the development of vertex sparsifiers, and shares important connections to several upcoming results in dynamic graph data structures, including online models. 

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