A Multi-Scale DNN Algorithm for Nonlinear Elliptic Equations with Multiple Scales

Algorithms based on deep neural networks (DNNs) have attracted increasing attention from the scientific computing community. DNN based algorithms are easy to implement, natural for nonlinear problems, and have shown great potential to overcome the curse of dimensionality. In this work, we utilize the multi-scale DNN-based algorithm (MscaleDNN) proposed by Liu, Cai and Xu (2020) to solve multi-scale elliptic problems with possible nonlinearity, for example, the p-Laplacian problem. We improve the MscaleDNN algorithm by a smooth and localized activation function. Several numerical examples of multi-scale elliptic problems with separable or non-separable scales in low-dimensional and high-dimensional Euclidean spaces are used to demonstrate the effectiveness and accuracy of the MscaleDNN numerical scheme.     

ASO Author Reflections: Is There a Relationship Between TIL and Regression in Melanoma?

Annals of Surgical Oncology -     

2‐deoxy D‐glucose treatment does not elicit a hair growth response in alopecia areata

2‐deoxy D‐glucose (2DG) was tested for efficacy in treating alopecia areata using the C3H/HeJ skin graft model. 2DG has proven to be efficacious in treatment of various mouse models of autoimmunity with minimal serious side effects noted. This agent has been shown to normalize abnormally activated T‐cell populations while also preventing cell surface expression of NKG2D; key factors defining alopecia areata disease progression. Daily oral ingestion of 2DG via drinking water to mice with patchy or diffuse alopecia areata for 16 weeks failed to prevent expansion of alopecia or cause regrowth of hair in treated mice. Histologically, there were no differences between treated and control groups. These results indicate that, while 2DG is effective for some autoimmune diseases, it was not efficacious for the cell‐mediated autoimmune mouse disease, alopecia areata.     

Worsening head bleeds in elderly blunt head trauma patients taking antithrombotics: Delayed CT head fails to change management

Background

Most elderly trauma patients suffer blunt head injury and many utilize antithrombotic (AT) medications. The utility of delayed CT-head (D-CTH) in neurologically intact elderly patients using AT who have an intracranial hemorrhage (ICH) on presentation is unknown. We hypothesized that D-CTH would not alter clinical management and aimed to evaluate the role of D-CTH in this population.