Search for publications listed at MathSciNet (citations)
Papers maintained at the Arxiv

(latest versions are always the pdf links)

In progress:

31. (with J. Sohl-Dickstein and K. Koepsell) Efficient and optimal binary Hopfield associative memory storage using minimum probability flow, NIPS Workshop on Discrete Optimization in Machine Learning (DISCML), 2012. pdf

(with L. Garcia-Puente and K. Talaska) Groebner bases and partial sums of Catalan numbers, in progress.


. (with N. Tran) Robust exponential memory in Hopfield networks, submitted. pdf | Python code | arxiv

28. (with S. Lin and A. Wibisono) Tight bounds on the infinity norm of inverses of symmetric diagonally dominant positive matrices, submitted. pdf

Science Related:

(with F. Sommer) When can dictionary learning uniquely recover sparse data from subsamples? IEEE Transactions on Information Theory, to appear. pdf

(with Ram Mehta and Kilian Koepsell) A Hopfield recurrent neural network trained on natural images performs state-of-the-art image compression, IEEE International Conference on Image Processing (ICIP), 2014, pp. 4092–4096.

(with G. Isely, and F. Sommer) Deciphering subsampled data: Adaptive compressive sampling as a principle of brain communication. Advances in Neural Information Processing Systems (NIPS) 23. Eds: J. Lafferty and C. K. I. Williams and J. Shawe-Taylor and R.S. Zemel and A. Culotta (2011) 910-918. pdf

1. (with W. Coulter, G. Isely, F. Sommer), Adaptive compressed sensing - a new class of self-organizing coding models for neuroscience, 2010 IEEE International Conference on Acoustics Speech and Signal Processing (ICASSP), 5494-5497. pdf

Mathematics Published:

(with A. Wibisono) A Hadamard-type lower bound for symmetric diagonally dominant positive matrices, Linear Algebra and Applications, 472 (2015) 135-141. pdf

(with L.H. Lim) Most tensor problems are NP-hard, Journal of the ACM, 60 (2013), no. 6, Art. 45, 39 pp. pdf | Ex 1.5 SINGULAR code | Appendix SINGULAR code, Macaulay 2 code

(with F. Sottile) Static skew-symmetric output feedback control, SIAM Journal on Control and Optimization, 51 (2013), Issue 4. pdf | arXiv

(with A. Martin del Campo) Finiteness theorems and algorithms for permutation invariant chains of Laurent lattice ideals, Journal of Symbolic Computation, 50 (2013) 314-334. pdf  | errata | Macaulay 2 code

(with L. Levine and D. Rhea) Equations solvable by radicals in a uniquely divisible group, Bulletin of the London Mathematical Society, (2012) 45 (1): 61-79. pdf | arXiv

(with O. Bastani, D. Popov, and J.M. Rojas) Randomization, sums of squares, near-circuits, and faster real root counting, Contemporary Mathematics volume dedicated to March 2010 BIRS workshop on Randomization, Relaxation, and Complexity, AMS Press, 2011. pdf

(with S. Sullivant) Finite Groebner bases in infinite dimensional polynomial rings and applications, Advances in Mathematics, 221 (2012) 1-25. pdf | arXiv

20. (with J. De Loera, P. Malkin, M. Omar) Recognizing Graph Theoretic Properties with Polynomial Ideals, Electronic Journal of Combinatorics, 17 (2010), 1-26. pdf

(with Garcia-Puente, Martin del Campo, Ruffo, Teitler, Johnson, and Sottile) Experimentation at the Frontiers of Reality in Schubert Calculus, Contemporary Mathematics, 517 (2010), 365-380. pdf | arXiv

Sums of polynomial squares over totally real fields are rational sums of squares, Proceedings of the American Mathematical Society, 137 (2009), 921-930. pdf

(with J. Nie) An elementary and constructive solution to Hilbert's 17th Problem for matrices, Proceedings of the American Mathematical Society, 136 (2008), 73-76. arxiv | pdf

(with T. Windfeldt). An algebraic characterization of uniquely vertex colorable graphs, Journal of Combinatorial Theory Series B, 98 (2008), 400-414. pdf | arXiv | code | slides

(with T. Windfeldt). Minimal generators for symmetric ideals, Proceedings of the American Mathematical Society, 136 (2008), 4135-4137. arxiv | pdf

(with S. Armstrong). Solvability of symmetric word equations in positive definite letters, Journal of the London Mathematical Society, 76 (2007), no. 3, 777-796. arXiv | pdf | maple code 1 | maple code 2

13. Advances on the Bessis-Moussa-Villani trace conjecture, Linear Algebra and Applications, 426 (2007), 130-142. arXiv | pdf | LinAlgAppl

12. (with L. Levine)  Polynomial recurrences and cyclic resultants, Proceedings of the American Mathematical Society, 135 (2007), 1607-1618.  arXiv | pdf | AMS

11. (with M. Aschenbrenner) Finite generation of symmetric ideals, Transactions of the American Mathematical Society, 359 (2007), 5171-5192; erratum, ibid. 361 (2009), 5627-5627.  arXiv | pdf | (minor errata here)

10. Cyclic Resultants, Journal of Symbolic Computation, 39 (2005), 653-669; erratum, ibid. 40 (2005), 1126–1127. arXiv | pdf | errata to print version

9. (with C. R. Johnson).  On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices, Journal of Statistical Physics, 118 (2005), 781-789. pdf | ps

8. (with D. L. Rhea).  A Result About the Density of Iterated Line Intersections in the Plane, Computational Geometry: Theory and Applications, 33 (2006), 106-114. arXiv (low res version) | pdf (high res version)

7. Appendix to the article "New Coins From Old: Computing With Unknown Bias," by E. Mossel and Y. Peres, Combinatorica, 25 (2005), 707-724. arXiv | pdf | ps

6. Logarithmic Derivatives of Solutions to Linear Differential Equations, Proceedings of the American Mathematical Society, 132 (2004), no. 9, 2693-2701. arXiv | pdf | ps | AMS (an expanded and more expository version is here).

5. (with C. R. Johnson).  Symmetric word equations in two positive definite letters, Proceedings of the American Mathematical Society 132 (2004), no. 4, 945-953. arXiv | pdf | ps

4. (with C. R. Johnson, Y. Harel, J. Groves, P. Rault). Absolutely flat idempotents, Electronic Journal of Linear Algebra, 10 (2003), pp. 190-200.  arxiv | pdf

3. (with C. R. Johnson).  Positive eigenvalues of generalized words in two Hermitian positive definite matrices, in: Novel Approaches to Hard Discrete Optimization (P. Pardalos and H. Wolkowicz, eds.), Fields Institute Communications 37, 2003, pp. 111-122. arxiv | pdf

2. (with C. R. Johnson). Eigenvalues of words in two positive definite letters, SIAM Journal of Matrix Analysis and Applications, 23 (2002), pp. 916-928.  arxiv | pdf

1. (with C. R. Johnson and I. M. Spitkovsky). Positive eigenvalues and two-letter generalized words, Electronic Journal of Linear Algebra, 9 (2002), pp. 21-26. arxiv | pdf


6. (with F. Sommer). Comment on the Article "Distilling free-form natural laws from experimental data", 2010. pdf | arXiv

(with T. Windfeldt). Fibonacci identities and graph colorings, Fibonaccci Quarterly, Fibonacci Quart. 46/47 (2008/09), pp. 220–224. pdf | arXiv

(with D. Rhea). Automorphisms of finite abelian groups, American Mathematical Monthly, 114 (2007), no. 10, 917-923. pdf | arXiv | Wikipedia

3. Uniqueness of degree 5 symmetric word equations. pdf

2. Relations between words in two positive definite letters. pdf | ps

1. University of California, Berkeley, Ph.D. Thesis, "Solving polynomial systems with special structure," 2005. pdf

Chris Hillar

Home | Articles | Research | Teaching | Problems | Expository