GeometryResearchOverviewJan2010

GeometryResearchOverviewJan2010 - Applied Algorithms...

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Unformatted text preview: Applied Algorithms Research Assoc. Prof Assoc Prof. Karen Daniels Channel Assignment for Telecommunications Design Analyze Covering for Geometric Modeling feasibility, estimation, optimization problems for covering, assignment, clustering, packing, layout, geometric modeling Data Mining, Clustering, for Bioinformatics Bi i f ti Apply Meshing for Geometric Modeling Packing for Manufacturing Courtesy of Cadence Design Systems Topological Invariant Estimation for Geometric Modeling g Covering: 2D Polygonal Covering [CCCG 2001,CCCG2003] 2001 CCCG2003] Input: Supported under NSF/DARPA CARGO program Covering polygons Q = {Q1, Q2 , ... , Qm} {Q Target polygons (or point-sets) P = {P1, P2 , ... , Pn} g p yg ( point- ) p {P Output: Translations = { 1, 2 , ... , m} such that P2 P1 Translational 2D Polygon Covering Q3 Q1 Q2 Q3 Q1 Translated Q Covers P Sample P and Q With graduate students R. Inkulu, A. Mathur, C.Neacsu, & UNH professor R. Grinde P P2 P1 1 j m U j ( Qj ) Q2 Covering: 2D B-Spline Covering [CORS/INFORMS2004, UMass Lowell Student Research Symposium 2004, Computers Graphics Forum, 2006] Supported under NSF/DARPA CARGO p g pp program Out T1 I S In E T2 With graduate student C. Neacsu Covering: Box Covering [12th WSEAS Int. Conf. on Computers, 2008] Int Conf Computers Supported under NSF/DARPA CARGO p g pp program Goal: Goal: Translate boxes to cover another box Orthotope ( ) covering in 2D, 3D, ... p (box) g , , 2D views of 3D covering Partial cover (red part uncovered) Full cover With Masters student B. England Covering: Covering Web Site http://www.cs.uml.edu/~kdaniels/covering/covering.htm http://www cs uml edu/~kdaniels/covering/covering htm With graduate student C. Neacsu and undergraduate A. Hussin Geometric Modeling: Estimating Topological Properties from a Point Sample [4th Int. Symp. on 3D Data Processing, Visualization and Transmission, 2008] Supported under NSF/DARPA CARGO program Euler characteristic: = #(components) - #(tunnels) + #(bubbles) Heart MRI data Cube with 3 crossing tunnels: = -4 Stanford bunny With graduate student C. Neacsu, UMass Amherst student B. Jones, UML Math Profs. Klain, Rybnikov, students N. Laflin, V. Durante Geometric Modeling: Mesh Generation for Finite Element Modeling [accepted as Research Note for 17th Int. Meshing Roundtable, 2008, and Fall CG Workshop, 2009] Needed for signal integrity in printed circuit board interconnect routing 2D constrained Delaunay triangulation is extruded into 3D to form triangular prism mesh Courtesy of Cadence Design Systems Doctoral student S. Ye Computational Geometry: Thrackle Extensibility [CCCG 2006] Thrackle: Drawing of a simple graph on the plane: each edge drawn as a smooth arc with distinct end-points, endevery two edges have exactly one common point, endpoints of each edge are two vertices; no edge crosses itself. Conway's thrackle conjecture: Number of edges for n vertices is at most n. With graduate student W. Li and Math Prof. Rybnikov Bioinformatics: Improved Support Vector Clustering [ICBA2004, SIAM Data Mining 2006, UMass Lowell Student Research Symposium 2003 ] Goal: Goal: Find natural groupings of data points Support Vector Clustering based on machine learning method With doctoral student S. Lee Information Sciences, Engineering and Technology ISET Research Scholars Program Faculty mentors F lt t Scholarship support Research Projects Sponsored by National Polygonal Covering Science Foundation Research Projects Optimizing Channel Allocation in Wireless Networks H. Rathi (2002-2003) (2002Modeling Hemoglobin Formation S. Kundu (2003) S. Rathi (2003) Flow N Fl Networks k S. Casey (2005) S. MacFarland (2005) A. Hussin (2005) Algorithm Efficiency A Singh (2006) A. Random Forests for Cancer Classification L. Liang (2006) Bioinformatics N. Laflin (2006) Topological Estimation N. Laflin, V. Durante (2006) f ( ) This program was funded by NSF from Fall, 2001 - Summer, 2007. Key Partners & Resources y Students: ScD, MS, undergrad Affiliations: Design Analyze CACT IVPR HCTAR Computers: SparcUltras, Sun Blades Blades, PCs feasibility, optimization problems for covering, assignment, clustering, i i t l t i packing, layout Apply Appl Algorithms & Geometry Related Applied Courses: Courses: 91.503, 91.504, Algorithms Al ith 91.404, 91.580 Lab: OS 220B Software Libraries: CPLEX, CGAL, LEDA ...
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This note was uploaded on 02/13/2012 for the course CS 91.504 taught by Professor Daniels during the Spring '10 term at UMass Lowell.

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