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1. A Parameterization of Local and Remote Tidal Mixing

   https://doi.org/10.1029/2020MS002065  

   de Lavergne, C.; Vic, C.; Madec, G.; Roquet, F.; Waterhouse, A. F.; Whalen, C. B.; Cuypers, Y.; Bouruet‐Aubertot, P.; Ferron, B.; Hibiya, T. (May 2020, Journal of Advances in Modeling Earth Systems)

   Abstract Vertical mixing is often regarded as the Achilles' heel of ocean models. In particular, few models include a comprehensive and energy‐constrained parameterization of mixing by internal ocean tides. Here, we present an energy‐conserving mixing scheme which accounts for the local breaking of high‐mode internal tides and the distant dissipation of low‐mode internal tides. The scheme relies on four static two‐dimensional maps of internal tide dissipation, constructed using mode‐by‐mode Lagrangian tracking of energy beams from sources to sinks. Each map is associated with a distinct dissipative process and a corresponding vertical structure. Applied to an observational climatology of stratification, the scheme produces a global three‐dimensional map of dissipation which compares well with available microstructure observations and with upper‐ocean finestructure mixing estimates. This relative agreement, both in magnitude and spatial structure across ocean basins, suggests that internal tides underpin most of observed dissipation in the ocean interior at the global scale. The proposed parameterization is therefore expected to improve understanding, mapping, and modeling of ocean mixing. 

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2. Variational Covariance Smoothing for Dynamic Functional Connectivity Analysis

   https://doi.org/10.1109/IEEECONF60004.2024.10942750  

   Abeysekara, Ruwanthi; Simon, Jonathan Z; Babadi, Behtash (October 2024, IEEE)

   Functional connectivity is among the widely used metrics to assess the network-level attributes of brain function. While most existing analysis frameworks assume static functional connectivity during the course of an experiment, to capture neural dynamics over short time scales, a time-varying notion of functional connectivity is required. By revealing how neural networks reconfigure in response to changing external stimuli, internal states, and task demands, time-varying functional connectivity can be leveraged to study flexible cognition, such as working memory, attention, and decision-making. A major challenge in estimating time-varying functional connectivity from high-dimensional neural is the associated computational complexity. Existing methods trade off accuracy for computational efficiency, especially in applications that require real-time or near real-time processing. Here, we build on existing work using covariance-domain state-space models and introduce a framework based on variational inference that allows low-complexity estimation of time-varying functional connectivity and construction of confidence intervals. We validate the performance of the proposed method using simulation studies. Our results reveal significant gains in computational complexity compared to existing methods, while maintaining high accuracy. 

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3. Role of Tropical Variability in Driving Decadal Shifts in the Southern Hemisphere Summertime Eddy-Driven Jet

   https://doi.org/10.1175/JCLI-D-19-0604.1  

   Yang, Dongxia; Arblaster, Julie M.; Meehl, Gerald A.; England, Matthew H.; Lim, Eun-Pa; Bates, Susan; Rosenbloom, Nan (July 2020, Journal of Climate)

   null (Ed.)

   Abstract The Southern Hemisphere summertime eddy-driven jet and storm tracks have shifted poleward over the recent few decades. In previous studies, explanations have mainly stressed the influence of external forcing in driving this trend. Here we examine the role of internal tropical SST variability in controlling the austral summer jet’s poleward migration, with a focus on interdecadal time scales. The role of external forcing and internal variability are isolated by using a hierarchy of Community Earth System Model version 1 (CESM1) simulations, including the pre-industrial control, large ensemble, and pacemaker runs. Model simulations suggest that in the early twenty-first century, both external forcing and internal tropical Pacific SST variability are important in driving a positive southern annular mode (SAM) phase and a poleward migration of the eddy-driven jet. Tropical Pacific SST variability, associated with the negative phase of the interdecadal Pacific oscillation (IPO), acts to shift the jet poleward over the southern Indian and southwestern Pacific Oceans and intensify the jet in the southeastern Pacific basin, while external forcing drives a significant poleward jet shift in the South Atlantic basin. In response to both external forcing and decadal Pacific SST variability, the transient eddy momentum flux convergence belt in the middle latitudes experiences a poleward migration due to the enhanced meridional temperature gradient, leading to a zonally symmetric southward migration of the eddy-driven jet. This mechanism distinguishes the influence of the IPO on the midlatitude circulation from the dynamical impact of ENSO, with the latter mainly promoting the subtropical wave-breaking critical latitude poleward and pushing the midlatitude jet to higher latitudes. 

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4. Networked Anti-coordination Games Meet Graphical Dynamical Systems: Equilibria and Convergence

   https://doi.org/10.1609/aaai.v37i10.26378  

   Qiu, Zirou; Chen, Chen; Marathe, Madhav V.; Ravi, S. S.; Rosenkrantz, Daniel J.; Stearns, Richard E.; Vullikanti, Anil (June 2023, Proceedings of the AAAI Conference on Artificial Intelligence)

   Evolutionary anti-coordination games on networks capture real-world strategic situations such as traffic routing and market competition. Two key problems concerning evolutionary games are the existence of a pure Nash equilibrium (NE) and the convergence time. In this work, we study these two problems for anti-coordination games under sequential and synchronous update schemes. For each update scheme, we examine two decision modes based on whether an agent considers its own previous action (self essential) or not (self non-essential) in choosing its next action. Using a relationship between games and dynamical systems, we show that for both update schemes, finding an NE can be done efficiently under the self non-essential mode but is computationally intractable under the self essential mode. We then identify special cases for which an NE can be obtained efficiently. For convergence time, we show that the dynamics converges in a polynomial number of steps under the synchronous scheme; for the sequential scheme, the convergence time is polynomial only under the self non-essential mode. Through experiments, we empirically examine the convergence time and the equilibria for both synthetic and real-world networks. 

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5. When Can We Treat Trajectories As Points?

   Duggirala, Parasara Sridhar; Sheehy, Donald (July 2017, Canadian Conference on Computational Geometry)

   In the formal verification of dynamical systems, one often looks at a trajectory through a state space as a sample behavior of the system. Thus, metrics on trajectories give important information about the different behavior of the system given different starting states. In the important special case of linear dynamical systems, the set of trajectories forms a finite-dimensional vector space. In this paper, we exploit this vector space structure to define (semi)norms on the trajectories, give an isometric embedding from the trajectory metric into low-dimensional Euclidean space, and bound the Lipschitz constant on the map from start states to trajectories as measured in one of several different metrics. These results show that for an interesting class of trajectories, one can treat the trajectories as points while losing little or no information. 

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