Recent Research of CMC Math/CS Faculty

The CMC math and CS faculty represent a wide range of research areas, including algebraic topology and knot theory, functional, harmonic, and complex analysis, probability and statistics, numerical analysis, PDEs, compressed sensing, mathematical finance, number theory, discrete geometry, programming languages, and database systems. Some of our work is done in collaboration with undergraduate and graduate students; in the list below * indicates an undergraduate coauthor.

Publication Activity in 2013

Asuman Aksoy (functional analysis)

(with G. Lewicki) Limit theorems for numerical index, Journal of Mathematical Analysis and Applications, vol. 398 no. 1 (2013) pp. 296–302

Lenny Fukshansky (number theory, discrete geometry)

(with G. Henshaw, P. Liao*, M. Prince*, X. Sun, S. Whitehead*) On well-rounded ideal lattices, II, International Journal of Number Theory, vol. 9 no. 1 (2013) pp. 139–154
Heights and quadratic forms: on Cassels' theorem and its generalizations, in "Diophantine methods, lattices, and arithmetic theory of quadratic forms" (W. K. Chan, L. Fukshansky, R. Schulze-Pillot, and J. Vaaler, eds.), Contemporary Mathematics, AMS vol. 587 (2013), pp. 77–94
Diophantine methods, lattices, and arithmetic theory of quadratic forms -- proceedings of a BIRS workshop (Editors: W. K. Chan, L. Fukshansky, R. Schulze-Pillot, J. D. Vaaler), Contemporary Mathematics, AMS vol. 587 (2013)
(with X. Sun) On the geometry of cyclic lattices, submitted for publication

Deanna Needell (compressed sensing, randomized algorithms, functional analysis, computational mathematics, probability, statistics)

(with R. Ward) Near-optimal compressed sensing guarantees for total variation minimization, to appear in IEEE Transactions on Image Processing
(with L. Demanet and N. Nguyen) Super-resolution via superset selection and pruning, Proc. 10th International Conf. on Sampling Theory and Applications (SAMPTA) 2013
(with A. Divekar) Using correlated subset structure for compressive sensing recovery, Proc. 10th International Conf. on Sampling Theory and Applications (SAMPTA) 2013
(with M. A. Davenport and M. B. Wakin) Signal Space CoSaMP for Sparse Recovery with Redundant Dictionaries, Signal Processing with Adaptive Sparse Structured Representations (SPARS) 2013

Publication Activity in 2012

Asuman Aksoy (functional analysis)
- (with G. Lewicki) Minimal projections with respect to various norms, Studia Mathematica, vol. 210 no. 1 (2012) pp. 1–16
Lenny Fukshansky (number theory, discrete geometry)

(with K. Petersen) On well-rounded ideal lattices, International Journal of Number Theory, vol. 8 no. 1 (2012) pp. 189–206
(with I. Aliev, M. Henk) Generalized Frobenius numbers: bounds and average behavior, Acta Arithmetica, vol. 155 no. 1 (2012), pp. 53–62
(with G. Henshaw, P. Liao*, M. Prince*, X. Sun, S. Whitehead*) On integral well-rounded lattices in the plane, Discrete and Computational Geometry, vol. 48 no. 3 (2012), pp. 735–748
Well-rounded zeta-function of planar arithmetic lattices, to appear in the Proceedings of the AMS

(with W. K. Chan, G. Henshaw) Small zeros of quadratic forms missing a union of varieties, submitted for publication

(with G. Henshaw) Height bounds over quaternion algebras, submitted for publication

David German (mathematical finance)

(with H. Schellhorn) A no-arbitrage model of liquidity in financial markets involving Brownian sheets, submitted for publication

Mark Huber (computational probability)

(with J. Law) Simulation reduction of the Ising model to general matchings, Electronic Journal of Probability, vol. 17 no. 33 (2012), 15 pp.
(with F. Mitha) Monotonic multigamma coupling for perfect sampling, Journal of Statistical Computation and Simulation, vol. 82 no. 4 (2012), pp. 603–622
Spatial Birth-Death-Swap chains, to appear in Bernoulli
Simulation reductions for the Ising model, to appear in Journal of Statistical Theory and Practice
Bound on the artificial phase transition for perfect simulation of hard core Gibbs processes, to appear in Involve
Approximation algorithms for the normalizing constant of Gibbs distributions, submitted for publication
(with S. Schott) Random Construction of Interpolating sets for high dimensional integration, submitted for publication
(with J. Banks*, E. McCall*, D. Rozenfeld*, and J. Xu*) Using TPA to count linear extensions, submitted for publication

Chiu-Yen Kao (numerical analysis, PDEs, scientific computing, mathematical biology)

(with W. Chen, C.-S. Chou) Lax-Friedrichs Fast Sweeping Methods for Steady State Problems for Hyperbolic Conservation Laws, to appear in Journal of Computational Physics
(with S. Su) Efficient Rearrangement Algorithms for Shape Optimization on Elliptic Eigenvalue Problems, to appear in Journal of Scientific Computing
(with Y. Wang) Central Schemes for the Modified Buckley-Leverett Equation, to appear in Journal of Computational Science
(with S. Su, T. White, M. Schmidt, and G. Sapiro) Geometric Computation of Human Gyrification Indexes from Magnetic Resonance Images, to appear in Human Brain Mapping
(with R. J. Giedt, D. R. Pfeiffer, A. Matzavinos, B. R. Alevriadou) Mitochondrial Dynamics and Motility Inside Living Vascular Endothelial Cell: Role of Bioenergetics, Annals of Biomedical Engineering, 40 (9), pages 1903-1916, 2012
(with C. Xue, C.-S. Chou, A. Friedman, and C. Sen) Propagation of Cutaneous Thermal Injury: A Mathematical Model, Wound Repair and Regeneration, 20(1), pages 114-122, 2012
(with H. A. Lewis, L. T. Sinnott, and M. D. Bailey) Changes in Ciliary Muscle Thickness During Accommodation in Children, Optometry and Vision Science, 89(5), pages 727-737, 2012
(with L. A. E. Lossing, L. T. Sinnott, K. Richdale, and M. D. Bailey) Measuring Ciliary Muscle Thickness Changes with Accomodation in Young Adults, Optometry and Vision Science, 89(5), Pages 719-726, 2012
(with M. Hintermuller, A. Laurain) Principal Eigenvalue Minimization for an Elliptic Problem with Indefinite Weight and Robin Boundary Conditions, Applied Mathematics and Optimization, 65, pages 111-146, 2012
(with W. Shen, and Y. Lou) Evolution of Mixed Dispersal in Periodic Environments, Discrete and Continuous Dynamical Systems B, 17, pages 2047-2072, 2012
(with Y. Kodama) Numerical Study of the KP Equation for Non-Periodic Waves, Mathematics and Computers in Simulation, 82, pages 1185-1218, 2012
(wtih A. Friedman, C.-W. Shih) Transcriptional Control in Cell Differentiation: Asymptotic Limit, Journal of Differential Equations, 252, pages 5679-5711, 2012

Art Lee (programming languages, database systems)

(with D. H. Lee, S. K. Cha) A performance anomaly detection and analysis framework for DBMS development, IEEE Transactions on Knowledge and Data Engineering, vol. 24, no. 8 (2012), pp. 1345–1360

Deanna Needell (compressed sensing, randomized algorithms, functional analysis, computational mathematics, probability, statistics)
- (with B. Cung*, T. Jin*, J. Ramirez*, A. Thompson*, C. Boutsidis) Spectral Clustering: An empirical study of Approximation Algorithms and its Application to the Attrition Problem, submitted for publication
- (with R. Ward) Total variation minimization for stable multidimensional signal recovery, submitted for publication
- (with J. A. Tropp) Paved with Good Intentions: Analysis of a Randomized Block Kaczmarz Method, to appear in Linear Algebra and its Applications
- (with M. A. Davenport and M. B. Wakin) Signal Space CoSaMP for Sparse Recovery with Redundant Dictionaries, submitted for publication
- (with R. Ward) Two-subspace Projection Method for Coherent Overdetermined Systems, to appear in the Journal of Fourier Analysis and Applications
- (with R. Ward) Two-subspace Projection Method for Coherent Overdetermined Systems, Technical Report, CMC Faculty Publications and Research Technical Report, Paper 35. DOI: 10.5642/tspmcos.2012.01
- (with R. Ward) Stable image reconstruction using total variation minimization, submitted for publication
- (with Y. C. Eldar and Y. Plan) Uniqueness Conditions For Low-Rank Matrix Recovery, Applied and Computational Harmonic Analysis, vol. 33, no. 2 (2012), pp. 309–314
Sam Nelson (algebraic topology, knot theory)

(with V. Rivera*) Quantum Enhancements of Involutory Birack Counting Invariants, submitted for publication
(with E. Cody*) Polynomial Birack Modules, submitted for publication
(with E. Watterberg*) Birack Dynamical Cocycles and Homomorphism Invariants, submitted for publication
(with J. Blankstein*, S. Kim*, C. Lepel*, N. Sanderson*) Virtual shadow modules and their link invariants, to appear in the International Journal of Mathematics
(with A. S. Crans, A. Henrich) Polynomial knot and link invariants from the virtual biquandle, submitted for publication
(with J. Hennig*) The column group and its link invariants, Journal Knot Theory Ramifications, vol. 21 no. 7 (2012), 1250063, 15 pp.
(with M. Elhamdadi) N-degeneracy in rack homology and link invariants, Hiroshima Mathematical Journal, vol. 42 no. 1 (2012), pp. 127–142
(with S. Aksoy*) Bikei, involutory biracks and unoriented link invariants, Journal Knot Theory Ramifications, vol. 21 no. 6 (2012), 1250045, 13 pp.
(with J. Ceniceros*) (t,s)-racks and their link invariants, International Journal of Mathematics, vol. 23 no. 3 (2012), 1250001, 19 pp.

Mike O'Neill (harmonic analysis, geometric function theory)
- (with G. Aarao) Sharp estimates in some inequalities of Zygmund type for Riesz transforms, Proceedings of the AMS, vol. 140 no. 12 (2012) pp. 4227–4233
- A geometric and stochastic proof of the twist point theorem, Publicacions Matematiques, vol. 56 no. 1 (2012) pp. 41–63