active subspace
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2021 ◽  
Vol 933 ◽  
Author(s):  
Marios-Andreas Nikolaidis ◽  
Petros J. Ioannou

We demonstrate that in plane Couette turbulence a separation of the velocity field in large and small scales according to a streamwise Fourier decomposition allows us to identify an active subspace comprising a small number of the gravest streamwise components of the flow that can synchronize all the remaining streamwise flow components. The critical streamwise wavelength, $\ell _{x c}$ , that separates the active from the synchronized passive subspace is identified as the streamwise wavelength at which perturbations to the time-dependent turbulent flow with streamwise wavelengths $\ell _x<\ell _{xc}$ have negative characteristic Lyapunov exponents. The critical wavelength is found to be approximately 130 wall units and obeys viscous scaling at these Reynolds numbers.


2021 ◽  
Vol 1 ◽  
Author(s):  
Liyan Pan ◽  
Yongchan Gao ◽  
Zhou Ye ◽  
Yuzhou Lv ◽  
Ming Fang

This paper addresses the detection of a signal belonging to several possible subspace models, namely, a union of subspaces (UoS), where the active subspace that generated the observed signal is unknown. By incorporating the persymmetric structure of received data, we propose three UoS detectors based on GLRT, Rao, and Wald criteria to alleviate the requirement of training data. In addition, the detection statistic and classification bound for the proposed detectors are derived. Monte-Carlo simulations demonstrate the detection and classification performance of the proposed detectors over the conventional detector in training-limited scenarios.


2021 ◽  
Author(s):  
Ishaan Batta ◽  
Anees Abrol ◽  
Zening Fu ◽  
Vince Calhoun

Here we introduce a multimodal framework to identify subspaces in the human brain that are defined by collective changes in structural and functional measures and are actively linked to demographic, biological and cognitive indicators in a population. We determine the multimodal subspaces using principles of active subspace learning (ASL) and demonstrate its application on a sample learning task (biological ageing) on a Schizophrenia dataset. The proposed multimodal ASL method successfully identifies latent brain representations as subsets of brain regions and connections forming co-varying subspaces in association with biological age. We show that Schizophrenia is characterized by different subspace patterns compared to those in a cognitively normal brain. The multimodal features generated by projecting structural and functional MRI components onto these active subspaces perform better than several PCA-based transformations and equally well when compared to non-transformed features on the studied learning task. In essence, the proposed method successfully learns active brain subspaces associated with a specific brain condition but inferred from the brain imaging data along with the biological/cognitive traits of interest.


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