Singular layer Physics Informed Neural Network method for Plane Parallel Flows

We construct in this article the semi-analytic Physics Informed Neural Networks (PINNs), called {\em singular layer PINNs} (or {\em sl-PINNs}), that are suitable to predict the stiff solutions of plane-parallel flows at a small viscosity. Recalling the boundary layer analysis, we first find the corrector for the problem which describes the singular behavior of the viscous flow inside boundary layers. Then, using the components of the corrector and its curl, we build our new {\em sl-PINN} predictions for the velocity and the vorticity by either embedding the explicit expression of the corrector (or its curl) in the structure of PINNs or by training the implicit parts of the corrector (or its curl) together with the PINN predictions. Numerical experiments confirm that our new {\em sl-PINNs} produce stable and accurate predicted solutions for the plane-parallel flows at a small viscosity

The Impact of Product innovation on Performance: The Influence of Uncertainty and Managerial Accounting Information Systems

This paper reports on a survey of Taiwanese high-tech firms, using a path analysis to examine the effects of managerial accounting information systems (MAIS) on the relationship between product innovation and organizational performance. Two of the major characteristics suggested by Chenhall and Morris (1986), broad scope and timeliness, are systematically related to the subject matter of this study, thus, employing these two characteristics to explore the connection between MAIS, product innovation and organizational performance. We find that product innovation has a positive effect on organizational performance through the use of MAIS, and find the extent of this positive effect is more significant in business environments marked by high levels of uncertainty. This study provides evidence to understand whether product innovation requires more extensive use of MAIS in highly uncertain environments and whether the use of MAIS can improve organizational performance. The results also help practicing managers realize the importance of MAIS in modern organizations and the benefits of using MAIS to the organization. Finally, we remind managers engaging in product innovation practices that they should place importance on the use of MAIS, because traditional cost control systems no longer help in solving the problems that are specific to the current, modern business environment

Interplay between Cell Migration and Neurite Outgrowth Determines SH2B1β-Enhanced Neurite Regeneration of Differentiated PC12 Cells

The regulation of neurite outgrowth is crucial in developing strategies to promote neurite regeneration after nerve injury and in degenerative diseases. In this study, we demonstrate that overexpression of an adaptor/scaffolding protein SH2B1β promotes neurite re-growth of differentiated PC12 cells, an established neuronal model, using wound healing (scraping) assays. Cell migration and the subsequent remodeling are crucial determinants during neurite regeneration. We provide evidence suggesting that overexpressing SH2B1β enhances protein kinase C (PKC)-dependent cell migration and phosphatidylinositol 3-kinase (PI3K)-AKT-, mitogen activated protein kinase (MAPK)/extracellular signal-regulated protein kinase (ERK) kinase (MEK)-ERK-dependent neurite re-growth. Our results further reveal a cross-talk between pathways involving PKC and ERK1/2 in regulating neurite re-growth and cell migration. We conclude that temporal regulation of cell migration and neurite outgrowth by SH2B1β contributes to the enhanced regeneration of differentiated PC12 cells