Statistical state dynamics of weak jets in barotropic beta-plane turbulence

Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (`zonostrophic instability') which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide ranges of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the asymmetric evolution for weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.Comment: 27 pages, 17 figure

Latent Alignment with Deep Set EEG Decoders

The variability in EEG signals between different individuals poses a significant challenge when implementing brain-computer interfaces (BCI). Commonly proposed solutions to this problem include deep learning models, due to their increased capacity and generalization, as well as explicit domain adaptation techniques. Here, we introduce the Latent Alignment method that won the Benchmarks for EEG Transfer Learning (BEETL) competition and present its formulation as a deep set applied on the set of trials from a given subject. Its performance is compared to recent statistical domain adaptation techniques under various conditions. The experimental paradigms include motor imagery (MI), oddball event-related potentials (ERP) and sleep stage classification, where different well-established deep learning models are applied on each task. Our experimental results show that performing statistical distribution alignment at later stages in a deep learning model is beneficial to the classification accuracy, yielding the highest performance for our proposed method. We further investigate practical considerations that arise in the context of using deep learning and statistical alignment for EEG decoding. In this regard, we study class-discriminative artifacts that can spuriously improve results for deep learning models, as well as the impact of class-imbalance on alignment. We delineate a trade-off relationship between increased classification accuracy when alignment is performed at later modeling stages, and susceptibility to class-imbalance in the set of trials that the statistics are computed on