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A Parallel Solver for 3-D Full-Stokes Ice Sheet Modeling: Simulation results of the temperature evolution of a Greenland ice sheet after 10 years (Ju et al.).

A Parallel Solver for 3-D Full-Stokes Ice Sheet Modeling: Zoom-in of a region close to the ice sheet edge (Ju et al.).

Time evolution of “trident”-shaped branched
tube formation
via fusion of uniluminal vascular
spheroids in a KMC simulation. Top: the
cross-sectional views. Red: smooth muscle
cells; Green: endothelial cells; Blue: lumen
particles (see enlargement). Bottom: the external
views. (Y. Sun, X. Yang and Q. Wang)

Computational Analysis of Biofabrication Morphogenesis of a Branching Vascular Construct: Vascular construct made of a layer-by-layer deposition in a designed Y-shape pattern (Q. Wang et al.).

Fifth Roots: Take a random walk in the complex plane starting from 0, each step an equiprobable fifth root of unity. Ten steps later, there's a circle centered at your destination whose area is proportional to your probability of being there. Other than two minor modifications (taking the fifth power of all points and inflating the atom at zero), this is the distribution of complex homogeneous eigenvalues of the all-ones 10X10X10X10X10X10 hypermatrix. (Joshua Cooper with Aaron Dutle.)

Monochromatic Boxes in Color Grids: What is the size of the smallest box (left) so that, if the elements are colored with two colors, there must be a nontrivial "subgrid" (right) all in one color? (See Cooper et al.)

Adaptivity and Variational Stabilization for Convection-Diffusion Equations: Every fourth adaptive cycle of Algorithm 1 with modification at the outflow boundary starting from cycle 3 for the test problem (3.25) with $\epsilon = 5 \cdot 10^{-3}$. The first row depicts the finite element solution $u _ h$. The second row displays the corresponding grids of $u _ h$. (See Cohen et al.)

Adaptive Petrov-Galerkin Methods for First Order Transport Equations: The 18th iterate of the adaptive solver and corresponding grid of model problem (6.1) with Algorithm 5.3 with $X _ h = P _ {1,T _ h}, Z _ h = P _ {3,T _ {h/8}}$ and $K = 9$ (See Dahmen et al.).

# Project Highlights

 PermutahedronGiven a graph, a designated source vertex x, a designated sink vertex y, and a nonnegative vector v of dimension equal to the number of vertices, when is it possible to find a set of vertex weights so that a random walk starting from x, taking random steps to neighbors of the current vertex with probabilities proportional to their weights, and ending at its first visit to y has expected vertex occupation times given by v? Allowing "infinite weights" -- vertices which are always preferable to others -- invites the definition of an unusual kind of space: one that is homeomorphic to the so-called "permutahedron". This image is the result of applying such a map to the two-dimensional version of this space, filled with the Hilbert curve to illustrate the resulting distortions. (Joshua Cooper with David Collins.) Digitizing Optical Sound TracksThe University of South Carolina Moving Image Research Collections (MIRC) is collaborating with research faculty from the University’s Interdisciplinary Mathematics Institute (IMI) to develop an open-source software application to directly reproduce the optical sound tracks of motion picture films from digital scans producing, as a result, a synchronized sound film file. For more information and to download the open-source software, please visit the project's website.

# News Highlights

 Dec 05 Temlyakov publishes article in IMI Preprint Series Dec 04 Temlyakov publishes article in IMI Preprint Series Nov 12 Temlyakov honored at the International Conference on Nonlinear Approximations and Applications Oct 04 Ivanov and Petrushev publish article in IMI Preprint Series Sep 16 Dove, Griggs, Kang and Sereni publish article in IMI Preprint Series Sep 06 Paula Vasquez joins IMI as its newest member Sep 06 Xinfeng Liu is awarded a National Science Foundation grant

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