(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) 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 |