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This paper presents the Dual Neural Network (DuNN) method, a physics-driven numerical method designed to solve elliptic partial differential equations and systems using deep neural network functions and a dual formulation. The underlying elliptic problem is formulated as an optimization of the complementary energy functional in terms of the dual variable, where the Dirichlet boundary condition is weakly enforced in the formulation. To accurately evaluate the complementary energy functional, we employ a novel discrete divergence operator. This discrete operator preserves the underlying physics and naturally enforces the Neumann boundary condition without penalization. For problems without reaction term, we propose an outer-inner iterative procedure that gradually enforces the equilibrium equation through a pseudo-time approach. 

We studied the least-squares ReLU neural network (LSNN) method for solving a linear advection-reaction equation with discontinuous solution in [Z. Cai et al., J. Comput. Phys., 443 (2021), 110514]. The method is based on a least-squares formulation and uses a new class of approximating functions: ReLU neural network (NN) functions. A critical and additional component of the LSNN method, differing from other NN-based methods, is the introduction of a properly designed and physics preserved discrete differential operator. In this paper, we study the LSNN method for problems with discontinuity interfaces. First, we show that ReLU NN functions with depth \(\lceil \log\_2(d+1)\rceil+1\) can approximate any \(d\)-dimensional step function on a discontinuity interface generated by a vector field as streamlines with any prescribed accuracy. By decomposing the solution into continuous and discontinuous parts, we prove theoretically that the discretization error of the LSNN method using ReLU NN functions with depth \(\lceil \log\_2(d+1)\rceil+1\) is mainly determined by the continuous part of the solution provided that the solution jump is constant. Numerical results for both two- and three-dimensional test problems with various discontinuity interfaces show that the LSNN method with enough layers is accurate and does not exhibit the common Gibbs phenomena along discontinuity interfaces. 

In this Letter, we propose and investigate a retroreflective optical integrated sensing and communication (RO-ISAC) system using orthogonal frequency division multiplexing (OFDM) and corner cube reflector (CCR). To accurately model the reflected sensing channel of the RO-ISAC system, both a point source model and an area source model are proposed according to the two main types of light sources that are widely used. Detailed theoretical and experimental results are presented to verify the accuracy of the proposed channel models and evaluate the communication and sensing performance of the considered RO-ISAC system. 

Abstract Domain users (DUs) with a knowledge base in specialized fields are frequently excluded from authoring virtual reality (VR)-based applications in corresponding fields. This is largely due to the requirement of VR programming expertise needed to author these applications. To address this concern, we developed VRFromX, a system workflow design to make the virtual content creation process accessible to DUs irrespective of their programming skills and experience. VRFromX provides an in situ process of content creation in VR that (a) allows users to select regions of interest in scanned point clouds or sketch in mid-air using a brush tool to retrieve virtual models and (b) then attach behavioral properties to those objects. Using a welding use case, we performed a usability evaluation of VRFromX with 20 DUs from which 12 were novices in VR programming. Study results indicated positive user ratings for the system features with no significant differences across users with or without VR programming expertise. Based on the qualitative feedback, we also implemented two other use cases to demonstrate potential applications. We envision that the solution can facilitate the adoption of the immersive technology to create meaningful virtual environments. 

Genes that regulate hormone release are essential for maintaining metabolism and energy balance. Egr1 encodes a transcription factor that regulates hormone production and release, and a decreased in growth hormones has been reported in Egr1 knockout mice. A reduction in growth hormones has also been observed in Nestin-Cre mice, a model frequently used to study the nervous system. Currently, it is unknown how Egr1 loss or the Nestin-Cre driver disrupt pituitary gene expression. Here, we compared the growth curves and pituitary gene expression profiles of Nestin-Cre-mediated Egr1 conditional knockout (Egr1cKO) mice with those of their controls. Reduced body weight was observed in both the Nestin-Cre and Egr1cKO mice, and the loss of Egr1 had a slightly more severe impact on female mice than on male mice. RNA-seq data analyses revealed that the sex-related differences were amplified in the Nestin-Cre-mediated Egr1 conditional knockout mice. Additionally, in the male mice, the influence of Egr1cKO on pituitary gene expression may be overridden by the Nestin-Cre driver. Differentially expressed genes associated with the Nestin-Cre driver were significantly enriched for genes related to growth factor activity and binding. Altogether, our results demonstrate that Nestin-Cre and the loss of Egr1 in the neuronal cell lineage have distinct impacts on pituitary gene expression in a sex-specific manner.