Symplectic Exact Solution for Stokes Flow in the Thin Film Coating Applications

The symplectic analytical method is introduced to solve the problem of the stokes flow in the thin film coating applications. Based on the variational principle, the Lagrangian function of the stokes flow is established. By using the Legendre transformation, the dual variables of velocities and the Hamiltonian function are derived. Considering velocities and stresses as the basic variables, the equations of stokes flow problems are transformed into Hamiltonian system. The method of separation of variables and expansion of eigenfunctions are developed to solve the governing equations in Hamiltonian system, and the analytical solutions of the stokes flow are obtained. Several numerical simulations are carried out to verify the analytical solutions in the present study and discuss the effects of the driven lids of the square cavity on the dynamic behavior of the flow structure

Controlled generation of switching dynamics among metastable states in pulse-coupled oscillator networks

This research was supported by the Aihara Project, the FIRST program from JSPS, initiated by CSTP, and CREST, JST. Y.C.L. was supported by ARO under Grant No. W911NF-14-1-0504. Z.C.D. was supported by the National Natural Science Foundation of China (No. 11432010). H.L.Z. was supported by “The Fundamental Research Funds for the Central Universities” (No. 3102014JCQ01036), and by the National Natural Science Foundation of China (No. 11502200). We also thank anonymous reviewers for their insightful and useful comments.Peer reviewedPublisher PD

LESS: Label-efficient Multi-scale Learning for Cytological Whole Slide Image Screening

In computational pathology, multiple instance learning (MIL) is widely used to circumvent the computational impasse in giga-pixel whole slide image (WSI) analysis. It usually consists of two stages: patch-level feature extraction and slide-level aggregation. Recently, pretrained models or self-supervised learning have been used to extract patch features, but they suffer from low effectiveness or inefficiency due to overlooking the task-specific supervision provided by slide labels. Here we propose a weakly-supervised Label-Efficient WSI Screening method, dubbed LESS, for cytological WSI analysis with only slide-level labels, which can be effectively applied to small datasets. First, we suggest using variational positive-unlabeled (VPU) learning to uncover hidden labels of both benign and malignant patches. We provide appropriate supervision by using slide-level labels to improve the learning of patch-level features. Next, we take into account the sparse and random arrangement of cells in cytological WSIs. To address this, we propose a strategy to crop patches at multiple scales and utilize a cross-attention vision transformer (CrossViT) to combine information from different scales for WSI classification. The combination of our two steps achieves task-alignment, improving effectiveness and efficiency. We validate the proposed label-efficient method on a urine cytology WSI dataset encompassing 130 samples (13,000 patches) and FNAC 2019 dataset with 212 samples (21,200 patches). The experiment shows that the proposed LESS reaches 84.79%, 85.43%, 91.79% and 78.30% on a urine cytology WSI dataset, and 96.88%, 96.86%, 98.95%, 97.06% on FNAC 2019 dataset in terms of accuracy, AUC, sensitivity and specificity. It outperforms state-of-the-art MIL methods on pathology WSIs and realizes automatic cytological WSI cancer screening.Comment: This paper was submitted to Medical Image Analysis. It is under revie