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Jie L. Liang

Undergraduate Majors:
McNair Mentor:
Dr. Xin Li, Department of Mathematics
Graduate School Plans:
Mathematics Ph.D

Jie L. Liang

Jie Liang moved to the United States from China after she finished high school. To further her education, she attends University of Central Florida majoring in mathematics as a first generation undergraduate. Because of her dedication to obtaining a Ph.D. degree in mathematics, she seeks research opportunities. In 2010, Jie participated in a year-long research project named GAUSS in UCF funded by NSF. She worked under Dr. Xin Li on applying reweighed least square method to face recognition and submitted their paper to Undergraduate Research Journal. In summer 2011, Jie conducted research with Dr. Garvan at University of Florida on number theory through the Summer Research Experience for Rising Senior program. Together with Dr. Andrews from Pennsylvania State University, they submitted their paper to Ramanujan Journal. As a senior, Jie is currently working on her Honors in the Major thesis with Dr. Li on approximation theory.

Title: Combinatorial Interpretations of Congruences for the SPT-Function

Conducted at University of Florida as part of the Summer Research Experience for Rising Seniors program in the summer of 2011

Mentor: Dr. Frank Garvan. Math Department, University of Florida
Participants: Jie Liang

Authors: G. Andrews, F. Garvan, and J. Liang

Abstract: Let spt(n) denote the total number of appearances of the smallest parts in all the partitions of n. In 1988, the second author gave new combinatorial interpretations of Ramanujan's partition congruences mod 5, 7 and 11 in terms of a crank for weighted vector partitions. In 2008, the first author found Ramanujan-type congruences for the spt-function mod 5, 7 and 13. We give new combinatorial interpretations of the spt-congruences mod 5 and 7. These are in terms of the same crank but for a restricted set of vector partitions. The proof depends on relating the spt-crank with the crank of vector partitions and the Dyson rank of ordinary partitions. We derive a number of identities for spt-crank modulo 5 and 7. We prove the surprising result that all the spt-crank coefficients are nonnegative.

Title: Disguised Face Recognition with Reweighted Algorithms

Conducted at University of Central Florida as part of the CSUMS program in the summer of 2010

Mentor: Dr. Xin Li. Math Department, University of Central Florida
Participants: Jie Liang, Enrique Ortiz, and James Wilson

Abstract: We proposed a face recognition paradigm using reweighted L2 minimization with hashing, whose recognition rates are comparable to the random projection using L1 minimization. Yet, our method is not only much faster than the standard compressive sensing method of Yang et al, but also robust to occlusion. We show that the sparse solution can be recovered with a high probability because hashing preserves the restrictive isometry property and reweighted L2 mirrors the L1 (i.e. L0) solution. Moreover, we present a theoretical analysis on the convergence of the proposed L2 approach. Experiments show a very promising recognition rate even with occlusion and significant speedup compared with the results of Wright et al.