Journal: NPJ Systems Biology and Applications

Article Title: A deep learning framework for quantitative analysis of actin microridges

doi: 10.1038/s41540-023-00276-7

Figure Lengend Snippet: a A magenta box demarcates the 2D sub-image of a skeletonized microridge branch for estimation of L p . b Microridge skeleton contours (blue) were smoothened using a Gaussian fit (red curve). The inset shows a microridge skeleton (blue line) with the endpoints of the contour (magenta) used to obtain the boundary trace that returned the discrete x–y coordinates. c A cubic spline interpolation on the Gaussian smoothened microridge trace contours preserved the sequence of points to give several intermediate points. d Tangent angle ( θ k ) along the length ( ℓ ) of the microridge. e Rescaled κ s along the length ( ℓ ) of the microridge contour. f Distribution of κ s of microridges from 1052 cells (293, 1084, and 125 from the flank, yolk, and head, respectively) fitted to a Gaussian distribution (red line trace), whose variance gives an estimate of the effective persistence length ( L p ) as ~6.1 μm.

Article Snippet: Gaussian curvature ( https://www.mathworks.com/matlabcentral/fileexchange/11168-surface-curvature ) was modified to compute the Gauss gradient with σ = 1.2 μm using ( https://www.mathworks.com/matlabcentral/fileexchange/8060-gradient-using-first-order-derivative-of-gaussian ) to extract the first and second derivatives at each point in the image.

Techniques: Sequencing

Journal: Numerical Algorithms

Article Title: VEMcomp: a Virtual Elements MATLAB package for bulk-surface PDEs in 2D and 3D

doi: 10.1007/s11075-024-01919-4

Figure Lengend Snippet: Numerical solution at the final time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$T=10$$\end{document} T = 10 of the S-RDS on the ellipsoid \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Gamma $$\end{document} Γ defined in , solved in VEMcomp on a mesh with 3990 nodes and meshsize \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$h \le 0.1$$\end{document} h ≤ 0.1 , whose exact value is not provided by DistMesh. Top row: component \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 (left) and component \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_2$$\end{document} v 2 (right). Bottom row: \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L^2$$\end{document} L 2 norm of time derivative of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 over time (left) and spatial average of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_1$$\end{document} v 1 over time (right)

Article Snippet: For example, for the case of triangulated surfaces in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}^3$$\end{document} R 3 with an empty boundary, VEMcomp is fully compatible with the triangulated surfaces generated by the well-known Matlab package DistMesh [ ]; Black-box solvers : For multiple classes of PDE problems, the library provides a black-box interface that allows the user to set the problem parameters, and returns the VEM or FEM numerical solution.

Techniques: