(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
30. (with L. Garcia-Puente
and K. Talaska) Groebner bases and partial sums
of Catalan numbers, in progress.
Submitted:
29. (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:**
4. (with F. Sommer) When can dictionary learning uniquely recover sparse data from subsamples? *IEEE Transactions on Information Theory*, to appear. pdf
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, pp. 4092–4096.
2. (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:
27. (with A. Wibisono) A Hadamard-type lower bound for symmetric diagonally dominant positive matrices, *Linear Algebra and Applications*, **472** (2015) 135-141. pdf
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, Macaulay 2 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 | errata | 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) 45 (1): 61-79. 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. Thesi*s, "Solving
polynomial systems with special structure,"
2005. pdf
Chris Hillar |