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Papers maintained at the Arxiv


(latest versions are always the pdf links)

In progress:

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

31.
(with L. Garcia-Puente and K. Talaska) Groebner bases and partial sums of Catalan numbers, in progress.


Submitted:

30
. (with N. Tran) Robust exponential memory in Hopfield networks, submitted. pdf | supplementary info | Python code | arxiv

29.
(with A. Wibisono) A Hadamard-type lower bound for symmetric diagonally dominant positive matrices, submitted. pdf

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

27.
(with F. Sommer) When can dictionary learning uniquely recover sparse data from subsamples? submitted. pdf


Science Related:

3.
(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.

2.
(with G. Isely, and F. Sommer) Decyphering 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:

26.
(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

25.
(with F. Sottile) Static skew-symmetric output feedback control, SIAM Journal on Control and Optimization, 51 (2013), Issue 4. pdf | arXiv

24.
(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 | Macaulay 2 code 

23.
(with L. Levine and D. Rhea) Equations solvable by radicals in a uniquely divisible group, Bulletin of the London Mathematical Society, 2012. pdf | arXiv

22.
(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

21.
(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

19.
(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

18.
Sums of polynomial squares over totally real fields are rational sums of squares, Proceedings of the American Mathematical Society, 137 (2009), 921-930. pdf

17.
(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

16.
(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

15.
(with T. Windfeldt). Minimal generators for symmetric ideals, Proceedings of the American Mathematical Society, 136 (2008), 4135-4137. arxiv | pdf

14.
(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


Other

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

5.
(with T. Windfeldt). Fibonacci identities and graph colorings, Fibonaccci Quarterly, Fibonacci Quart. 46/47 (2008/09), pp. 220–224. pdf | arXiv

4.
(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

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