IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

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.).

Cluster analysis: indicating 9 separate clusters based upon percentage in poverty, percentage uninsured, and percentage unemployed, displayed according to their geographic location. (See K.J. Bennett, M. Yuen and F. Blanco-Silva)

# Project Highlights

 IMI - from Foundations to Challenging ApplicationsA video overview of the IMI created as one of the WEB TV materials of the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019). Evaluating Geodetic QuantitiesA team from the University's Interdisciplinary Mathematics Institute (IMI) has developed an algorithm and software in FORTRAN and MATLAB for fast and accurate evaluation of gravimetric quantities represented in high degree (> 2000) spherical harmonics at arbitrary scattered points in the space above the surface of the Earth. For more information and to download the program, visit the project's website. 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

 Jun 01 Paula Vasquez is awarded an NSF CAREER grant. May 31 Joshua Cooper Publishes New Book on Discrete Mathematics May 23 Qi Wang is awarded a National Science Foundation grant May 18 Joshua Cooper is awarded a grant from EpiCypher, Inc. Apr 30 Xiaofeng Yang is awarded a VPR ASPIRE-I grant Apr 10 Blanco-Silva co-authors paper in Journal of Rural Studies Feb 16 Pencho Petrushev is awarded a National Geospatial Agency grant

 Congratulations to our 2018 SPARC Graduate Research Grant Recipients!Each year, the Office of the Vice President for Research offers the SPARC (Support to Promote Advancement of Research and Creativity) Graduate Research Grant program for graduate students from all areas of study. This merit-based award funds the most competitive applications for research, creative or other meritorious scholarly projects, providing up to $5,000 to each successful graduate student applicant.Of the 54 students from 10 different academic units who have been awarded SPARC grants for 2017-2018, 4 are from the Department of Mathematics (see SPARC recipients: ): Candace Bethea, The Degree Map in Algebraic Geometry, Advisor: Jesse Kass Alicia Lamarche, Exceptional Collections of the Toric Variety Associated to$D _ 4\$, Advisor: Matthew BallardHays Whitlatch, Phylogenetic Distribution of Mitochondrial Genome, Advisor: Joshua Cooper, IMIDuncan Wright, Entropy of Quantum Random Walks, Advisor: George AndroulakisCONGRATULATIONS to Candace, Alicia, Hays and Duncan! "Reel Life" with Greg WilsbacherGreg Wilsbacher (University Libraries), lead-PI on a project with Pencho Petrushev (IMI), was featured in a video interview for @UofSC, where he discusses the University of South Carolina Moving Image Research Collections -- considered one of the top 10 archives of its type in the nation -- and specifically, the Fox Movietone News collection, which he curates. Wilsbacher is working with a team from 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. CAS Research Computing CenterThe College of Arts and Sciences (CAS) Research Computing Center (RCC) provides high performance computing and visualization resources (including assistance with the Computational Graphics Lab of the IMI), access to software, workshops, one-on-one consulting with domain experts, and complete data management strategies to researchers across all departments and divisions within the College. For more information, please contact the Head of Research Computing, Jun Zhou ( Zhouj@mailbox.sc.edu ) or visit:http://artsandsciences.sc.edu/technology/researchhome