Claire Ralph

  • Academic Institution: Cornell University
  • Program Year: 4
  • Practicum(s):
    Sandia National Laboratories, New Mexico (2010)
    Sandia National Laboratories, New Mexico (2011)
  • Degree(s):
    B.S. Chemistry, B.S. Mathematics, University of New Mexico, 5/2007
  • Field of Study: Theoretical Chemistry
  • Academic Advisor: Greg Ezra

Summary of Research:

My thesis research is in developing efficient, highly parallel algorithms for quantum mechanical computations. The wavefunction of a quantum mechanical system, such as a molecule, can be represented in many theoretically equivalent ways. However, many of these representations are computationally difficult to work with. I am currently developing a time evolution algorithm which relies upon a particularly efficient underlying representation of the wavefunction, known as a Matrix Product State (MPS). The use of MPS in quantum chemistry is relatively recent and has shown to be very suitable for parallel computations. A few time evolution algorithms for MPS exist, but each has pitfalls. Our new algorithm promises to avoid these pitfalls while scaling well.

My other area of interest is in developing algorithms for large graph problems. I am currently developing an algorithm for the subgraph isomorphism problem which targets multithreaded shared memory platforms such as the Cray XMT. Currently large graph problems are tackled by partitioning the graph into multiple memory domains. If a match exists within a memory domain, this technique can be very effective. Finding a good partitioning can be hard, however. The increase in availability of shared memory machines allows us the opportunity to avoid this partitioning step. We hope to develop competitive graph-matching algorithms for these machines. Our preliminary work shows promise of high scalability and effective use of the multithreading capabilities of these new architectures.

Publications:

Books:
Claire C Ralph and Santiago Simanca; Arithmetic Differential Operators over the p-adic Integers; LMS Lecture Notes; Cambridge University Press; 2012.

Papers:
J. Kinder, C. C. Ralph, G. K-L Chan; Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States; submitted. arXiv:1103.2155.
C. C. Ralph, V. J. Leung, W. McLendon; Subgraph Isomorphism for Multithreaded Shared Memory Architectures; In Proc. of the 24th ACM Symposium on Parallelism in Architectures and Algorithms; pp 71-74; 2012.
A. Buium, C. C. Ralph, S. R. Simanca; Arithmetic differential operators on the p-adic integers; Journal of Number Theory; vol. 131; iss 1; 2011.

Awards:

Summa cum laude, U of New Mexico, 2007
Highest honors, Department of Mathematics, U of New Mexico, 2007
Honors, Department of Chemistry, U of New Mexico, 2007
Outstanding Bachelor of the Year in Pure Mathematics, U of New Mexico, 2007
Regent's Scholarship (Highest scholarship awarded by the University), U of New Mexico, 2003-2007
Joan Willard Hemsing Tinco Scholarship, Chemistry Department, U of New Mexico, 2007
Thomas Whaley Endowed Memorial Award Summer Scholarship for Undergraduate Summer Research in Chemistry, U of New Mexico, 2006