662 research outputs found
Integration factor combined with level set method for reaction-diffusion systems with free boundary in high spatial dimensions
For reaction-diffusion equations in irregular domain with moving boundaries,
the numerical stability constraints from the reaction and diffusion terms often
require very restricted time step size, while complex geometries may lead to
difficulties in accuracy when discretizing the high-order derivatives on grid
points near the boundary. It is very challenging to design numerical methods
that can efficiently and accurately handle both difficulties. Applying an
implicit scheme may be able to remove the stability constraints on the time
step, however, it usually requires solving a large global system of nonlinear
equations for each time step, and the computational cost could be significant.
Integration factor (IF) or exponential differencing time (ETD) methods are one
of the popular methods for temporal partial differential equations (PDEs) among
many other methods. In our paper, we couple ETD methods with an embedded
boundary method to solve a system of reaction-diffusion equations with complex
geometries. In particular, we rewrite all ETD schemes into a linear combination
of specific {\phi}-functions and apply one start-of-the-art algorithm to
compute the matrix-vector multiplications, which offers significant
computational advantages with adaptive Krylov subspaces. In addition, we extend
this method by incorporating the level set method to solve the free boundary
problem. The accuracy, stability, and efficiency of the developed method are
demonstrated by numerical examples.Comment: 20 pages, 6 figures, 2 table
Numerical Methods for a Two-Species Competition-Diffusion Model With Free Boundaries
The systems of reaction-diffusion equations coupled with moving boundaries defined by Stefan condition have been widely used to describe the dynamics of spreading population and with competition of two species. To solve these systems numerically, new numerical challenges arise from the competition of two species due to the interaction of their free boundaries. On the one hand, extremely small time steps are usually needed due to the stiffness of the system. On the other hand, it is always difficult to efficiently and accurately handle the moving boundaries especially with competition of two species. To overcome these numerical difficulties, we introduce a front tracking method coupled with an implicit solver for the 1D model. For the general 2D model, we use a level set approach to handle the moving boundaries to efficiently treat complicated topological changes. Several numerical examples are examined to illustrate the efficiency, accuracy and consistency for different approaches
Beyond Universal Transformer: block reusing with adaptor in Transformer for automatic speech recognition
Transformer-based models have recently made significant achievements in the
application of end-to-end (E2E) automatic speech recognition (ASR). It is
possible to deploy the E2E ASR system on smart devices with the help of
Transformer-based models. While these models still have the disadvantage of
requiring a large number of model parameters. To overcome the drawback of
universal Transformer models for the application of ASR on edge devices, we
propose a solution that can reuse the block in Transformer models for the
occasion of the small footprint ASR system, which meets the objective of
accommodating resource limitations without compromising recognition accuracy.
Specifically, we design a novel block-reusing strategy for speech Transformer
(BRST) to enhance the effectiveness of parameters and propose an adapter module
(ADM) that can produce a compact and adaptable model with only a few additional
trainable parameters accompanying each reusing block. We conducted an
experiment with the proposed method on the public AISHELL-1 corpus, and the
results show that the proposed approach achieves the character error rate (CER)
of 9.3%/6.63% with only 7.6M/8.3M parameters without and with the ADM,
respectively. In addition, we also make a deeper analysis to show the effect of
ADM in the general block-reusing method
Expansion of Breast Cancer Stem Cells with Fibrous Scaffolds
Cancer stem cells (CSCs) are hypothesized as tumor-initiating cells within tumors and main contributors of tumor growth, metastasis and recurrence. Mammary cancer cells, MCF-7 cells, were cultured on 3D polycaprolactone (PCL) fibrous scaffolds, showing an increased proportion of CSCs. The expression of stem cell markers, including OCT3/4 and SOX2, and breast CSC-specific markers, SOX4 and CD49f, was significantly upregulated, and the mammosphere-forming capability in cells cultured on PCL fibrous scaffolds increased. The fibrous scaffolds also induced the elongation of MCF-7 cells and extended cell proliferation. The increase of CSC properties after being cultured on fibrous scaffolds was further confirmed with two luminal-type mammary cell lines, T47D and SK-BR-3, and a basal-type cell line, MDA-MB-231, by ALDEFLUOR assay and mammosphere formation assay. Moreover, we observed the upregulation of epithelial to mesenchymal transition and increased invasive capability in cells cultured on PCL fibrous scaffolds. These data suggest that the increase of CSC proportion in a 3D culture system may account for the enhanced malignancy. Therefore, our PCL fibrous scaffolds can potentially be used for CSCs enrichment and anti-cancer drug screening
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