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.

- 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
- (with S. Jin) The apple doesn't fall far from the (metric) tree: the equivalence of definitions, submitted for publication
- (with Z. Ibragimov) The Urysohn universal metric space and hyperconvexity, submitted for publication
- (with J. M. Almira) On Shapiro's lethargy theorem and some applications, submitted for publication
- (with J. M. Almira) On approximation schemes and compactness, submitted for publication
- (with Z. Glassman, O. Kosheleva and V. Kreinovich) From Urysohn’s universal
metric space to a universal space-time, submitted for publication

- Lenny Fukshansky (number theory, discrete geometry)
- Well-rounded zeta-function of planar arithmetic lattices, Proceedings of the American Mathematical Society, vol. 142 no. 2 (2014), pg. 369–380
- (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 W. K. Chan, G. Henshaw) Small zeros of quadratic forms missing a union of varieties, Transactions of the AMS, vol. 366 no. 10 (2014), pg. 5587--5612
- (with G. Henshaw) Lattice point counting and height bounds over number fields and quaternion algebras, Online Journal of Analytic Combinatorics, vol. 8 (2013), art. 4, 20 pp.
- (with H. Maharaj) Lattices from elliptic curves over finite fields, Finite Fields and Their Applications, vol. 28 (July 2014), pg. 67--78
- (with X. Sun) On the geometry of cyclic lattices, Discrete and Computational Geometry, vol. 52 no. 2 (2014), pg. 240--259
- Stability of ideal lattices
from quadratic number fields, to appear in the Ramanujan
Journal

- (with W. K. Chan, G. Henshaw) Totally isotropic subspaces of small height in quadratic spaces, to appear in Advances in Geometry
- (with A. Boettcher, S. R. Garcia, H. Maharaj) On lattices generated by finite Abelian groups, submitted for publication
- (with A. Boettcher, S. R. Garcia, H. Maharaj) Toeplitz determinants with perturbations in the corners, submitted for publication
- (with S. R. Garcia, X. Sun) Permutation invariant
lattices, submitted
for publication

- Mark Huber
(computational
probability)
- Bound on the artificial phase transition for perfect simulation of hard core Gibbs processes, Involve,5(3), pp. 247–255, 2013
- Nearly optimal Bernoulli factories for linear functions, submitted for publication, arXiv:1308.1562, 2013
- (with N. Marić) Simulation of multivariate distributions with fixed marginals and correlations, submitted for publication, 2013
- (with S. Schott) Random Construction of Interpolating sets for high dimensional integration, to appear, Journal of Applied Probability

- Chiu-Yen Kao (numerical analysis, PDEs, scientific computing, mathematical biology)
- (with S. E. Mous, C. Karatekin, I. Gottesman, D. Posthuma,
and T. J. H. White) Gyrification
differences in Children and Adolescents with
Velocardiofacial Syndrome and
Attention-Deficit/Hyperactivity Disorder: A Pilot Study,
to appear in Psychiatry Research Neuroimaging

- (with M. K. Kuchem, L. Sinnott, and M. D. Bailey) Ciliary
Muscle Thickness in Anisometropia, to appear in
Optometry and Vision Science

- (with Y. Wang) Bounded Domain
Problem for the Modified Buckley-Leverett Equation,
to appear in Journal of Dynamics and Differential
Equations

- (with A. Friedman, and R. Leander) On
the Dynamics of Radially Symmetric Granulomas,
Journal of Mathematical Analysis and Applications,
412(2), pages 776-791, 2014

- (with B. Osting) Minimal
Convex Combinations of Three Sequential
Laplace-Dirichlet Eigenvalues, Applied Mathematics
and Optimization, 69(1), pages 123-139, 2014

- (with B. Cockburn and F. Reitich) An
Adaptive Spectral/DG Method for a Reduced-Phase Space
Based Level Set Approach to Geometrical Optics on Curved
Elements, Journal of Computational Physics,
259, pages 636-649, 2014

- (with A. D. Pucker, L. T. Sinnott, and M. D. Bailey) Region-specific
relationships between refractive error and ciliary
muscle thickness in children, Journal of
Investigative Ophthalmology & Visual Science,
54 (7), pages 4710-4716, 3, 2013

- (with M. D. Bailey) Detection and measurement of
tissue images, US Patent App. 13/757, 243,
2013

- (with W. Chen, K. Diest, D. E. Marthaler, L. A. Sweatlock,
and S. Osher ) Gradient
Based Optimization Methods for Metamaterial Design,
Numerical Methods for Metamaterial Design, pages
175-204, 2013

- (with B. Osting) Minimal convex combinations of sequential Laplace-Dirichlet eigenvalues, SIAM Journal of Scientific Computation, 35(3), pages B731-B750, 2013
- (with X. Feng and T. Lewis) Convergent finite difference methods for one-dimensional fully nonlinear second order partial differential equations, Journal of Computational and Applied Mathematics, 254, pages 81-98, 2013
- (with S. Su, T. White, M. Schmidt, and G. Sapiro ) Geometric computation of human gyrification indexes from magnetic resonance images, Human Brain Mapping, 34(5), pages 1230-1244, 2013
- (with K. Richdale, L. T. Sinnott, M. A. Bullimore, P. Wassenaar, P. Schmalbrock, S. Patz, D. Mutti, A. Glasser, K. Zadnik ) Quantification of age-related and per diopter accommodative changes of the lens and ciliary muscle in the emmetropic human eye, Investigative Ophthalmology & Visual Science, 54(2), pages 1095-1105, 2013
- (with S. Su) Efficient rearrangement algorithms for shape optimization on elliptic eigenvalue problems, Journal of Scientific Computing, 54, pages 492-512, 2013
- (with W. Chen, C.-S. Chou) Lax-Friedrichs fast sweeping methods for steady state problems for hyperbolic conservation laws, Journal of Computational Physics, 234, pages 452-471, 2013
- (with Y. Wang) Central schemes for the
modified Buckley-Leverett equation, Journal of Computational
Science, 4, pages 12-23, 2013

- David Krumm
(number
theory, arithmetic geometry)

- Computing points of bounded
height in projective space over a number field,
submitted for publication

- (with J. Doyle) Computing algebraic numbers of bounded height, to appear in Mathematics of Computation
- (with J. Doyle, X. Faber) Preperiodic
points for quadratic polynomials over quadratic fields,
to appear in New York
Journal of Mathematics

- Art Lee (programming languages, database systems)
- (with J. Lee, Y.S. Kwon, F. Faerber, M. Muehle, C.
Bensberg, J.Y. Lee, W. Lehner) SAP
HANA distributed in-memory database system: transaction,
session, and metadata management, Proc. IEEE 29th International
Conference on Data Engineering (ICDE), 2013

- Deanna Needell (compressed sensing, randomized algorithms, functional analysis, computational mathematics, probability, statistics)
- (with R. Baraniuk, S. Foucart, Y. Plan, and M. Wootters)
Exponential decay of reconstruction error from binary
measurements of sparse signals, submitted for publication

- (with N. Nguyen and T. Woolf)
Linear Convergence of Stochastic Iterative Greedy
Algorithms with Sparse Constraints, submitted for publication

- (with J. Briskman*)
Block Kaczmarz Method with Inequalities, submitted for publication

- (with R. Zhao and A. Zouzias)
Randomized Block Kaczmarz Method with Projection for
Solving Least Squares,
submitted for publication

- (with A. Ma, A. Flenner, and A. Percus )
Improving Image Clustering using Sparse Text and the
Wisdom of the Crowds,
Proc. Asilomar Conference on Signals, Systems, and
Computers, Pacific Grove CA, Nov. 2014, to appear.

- (with R. Zhao, C. Johansen, and J.L. Grenard)
A Comparison of Clustering and Missing Data Methods for
Health Sciences,
Proc. Asilomar Conference on Signals, Systems, and
Computers, Pacific Grove CA, Nov. 2014, to appear.

- (with N. Sbrero and R. Ward)
Stochastic Gradient Descent, Weighted Sampling, and the
Randomized Kaczmarz algorithm, submitted for publication

- (with R. Giryes)
Near Oracle Performance of Signal Space Greedy Methods, submitted for publication

- (with G. Chen and A. Divekar) Guaranteed
sparse signal recovery with highly coherent sensing
matrices, to appear
in Sampling Theory in Signal Analysis and Image Processing

- (with N. Sbrero and R. Ward) Stochastic
gradient descent and the randomized Kaczmarz algorithm, submitted for publication

- (with R. Giryes) Greedy signal space
methods for incoherence and beyond, Applied and Computational
Harmonic Analysis, to appear

- (with Y. Ma and D. Baron) Two-part reconstruction in compressed sensing, submitted for publication
- (with N. Jamil, J. Muller, C. Lutteroth, and G. Weber) Kaczmarz algorithm with soft constraints for user interface layout, IEEE International Conference on Tools with Artificial Intelligence (ICTAI), 2013
- (with N. Lenssen*) On the mathematics of music: from chords to Fourier analysis, Journal of Humanistic Mathematics, vol. 4, iss. 1, pp 72-91, 2014
- (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) Near-optimal compressed
sensing guarantees for total variation minimization,
IEEE Transactions on Image
Processing, vol. 22, iss. 10, pp. 3941 - 3949, 2013

- (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

- Sam Nelson (algebraic topology, knot theory)
- (with A. S. Crans, A. Henrich) Polynomial knot and link invariants from the virtual biquandle, J. Knot Theory Ramifications 22 (2013), no. 4, 134004, 15 pp.
- (with J. Ceniceros*) Twisted virtual biracks and their twisted virtual link invariants, Topology Appl. 160 (2013), no. 2, 421–429
- Link invariants from finite biracks, to appear in Banach Center Proceedings
- Link invariants from finite racks, to appear in Fundamenta Mathematicae
- (with K. Pelland*) Birack shadow modules and their link invariants, to appear in J. Knot Theory Ramifications

- Asuman Aksoy
(functional
analysis)

- (with G. Lewicki) Minimal
projections with respect to various norms, Studia Mathematica,
vol. 210 no. 1 (2012) pp. 1–16

- (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

- 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, Bernoulli 18(3), pp. 1031–1041, 2012
- Approximation algorithms for the normalizing constant of Gibbs distributions, submitted for publication, arXiv:1206.2689, 2012
- (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 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

- (with R. Ward) Total variation
minimization for stable multidimensional signal
recovery, submitted for publication
- 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 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