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https://www.selleckchem.com/products/deg-77.html Mean field games (MFG) and mean field control (MFC) are critical classes of multiagent models for the efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory, industrial engineering, crowd motion, and more. In this paper, we provide a flexible machine learning framework for the numerical solution of potential MFG and MFC models. State-of-the-art numerical methods for solving such problems utilize spatial discretization that leads to a curse of dimensionality. We approximately solve high-dimensional problems by combining Lagrangian and Eulerian viewpoints and leveraging recent advances from machine learning. More precisely, we work with a Lagrangian formulation of the problem and enforce the underlying Hamilton-Jacobi-Bellman (HJB) equation that is derived from the Eulerian formulation. Finally, a tailored neural network parameterization of the MFG/MFC solution helps us avoid any spatial discretization. Our numerical results include the approximate solution of 100-dimensional instances of optimal transport and crowd motion problems on a standard work station and a validation using a Eulerian solver in two dimensions. These results open the door to much-anticipated applications of MFG and MFC models that are beyond reach with existing numerical methods.The invasive behavior of glioblastoma is essential to its aggressive potential. Here, we show that pleckstrin homology domain interacting protein (PHIP), acting through effects on the force transduction layer of the focal adhesion complex, drives glioblastoma motility and invasion. Immunofluorescence analysis localized PHIP to the leading edge of glioblastoma cells, together with several focal adhesion proteins vinculin (VCL), talin 1 (TLN1), integrin beta 1 (ITGB1), as well as phosphorylated forms of paxillin (pPXN) and focal adhesion kinase (pFAK). Confocal microscopy specifically localiz

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