Tackling the curse of dimensionality with physics-informed neural networks.

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional partial differential equations (PDEs), as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerical PDEs in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs' and PINNs' residual into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schrödinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in less than one hour for 1000 dimensions and in 12 h for 100,000 dimensions on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.

Effects of age and flight experience on prefrontal cortex activity in airline pilots: An fNIRS study.

It is essential for airlines to have a deep understanding of the cognitive impact of aging among pilots. The current literature on executive function indicates that compensatory mechanisms in the brain may counteract age-related cognitive decline, at least up to certain task load levels. However, few studies have been administered to evaluate changes in aircrew competence as they age. The present study focuses on dorsolateral prefrontal cortex (DLPFC) activity as it is implicated in cognitive performance and working memory, which are associated with skill proficiency. We measured the DLPFC activity for airline pilots, including trainees, during maneuvering using a flight simulator. Our preliminary results indicated that only expert (aged) pilots demonstrated higher activity of the left DLPFC than the right one. However, for youth trainees, not only was the error rate high while using the flight simulator, but the activity of the DLFPC was also lower than that of the expert pilots, and there was no statistically significant difference between the left and right DLPFC. Although these findings partially differ from those reported in previous studies on age-related changes, it is evident that training as an airline pilot for over 20 years may affect such results. We believe that this noninvasive approach to objective quantification of skill will facilitate the development of effective assessment competence in aging.

Predominance of T-bet-positive Th1 cells in infiltrating T-lymphocytes in most of active arteritis lesions of giant cell arteritis.

Immunological mechanisms through the activation of CD4-positive T-cells have been assumed to be involved in the pathogenesis of giant cell arteritis (GCA). Many studies employing frozen tissues of temporal artery biopsy, peripheral blood lymphocytes, and plasma of GCA patients have revealed the contribution of interferon-γ and interleukin-17 in both protein and mRNA levels. However, the analyses using formalin-fixed and paraffin-embedded (FFPE) tissue specimens, in which the correlation between histopathologic pictures and immunological circumstances would be elucidated, have been limited. Here, we performed the immunohistochemical analyses of infiltrating small lymphocytes in GCA lesions using FFPE specimens, especially of the subsets of CD4-positive T-cells by immunohistochemistry with antibodies against T-bet, GATA-3, RORγT, and Foxp3, which is the differentiation-specific transcription factor for Th1, Th2, Th17, and Treg cells, respectively. In these slides, the nuclear-positive staining is much more clearly and easily identifiable than the cytoplasmic staining for cytokines. The results indicate the predominance of T-bet-positive Th1 cells in infiltrating T-cells in most of active arteritis lesions of GCA. Furthermore, our data suggest the possible immunosuppressive microenvironment induced by T-reg cells and M2-type macrophages in the arteritis lesions throughout the course of GCA inflammation.