Filter Results:
- Full text PDF available (42)
Publication Year
2001
2018
- This year (2)
- Last 5 years (15)
- Last 10 years (39)
Publication Type
Co-author
Journals and Conferences
Learn More
- Christopher J. Hillar, Lek-Heng Lim
- J. ACM
- 2013
We prove that multilinear (tensor) analogues of many efficiently computable problems in numerical linear algebra are NP-hard. Our list includes: determining the feasibility of a system of bilinear… (More)
Let A be a commutative Noetherian ring, and let R = A[X] be the polynomial ring in an infinite collection X of indeterminates over A. Let SX be the group of permutations of X. The group SX acts on R… (More)
- Charles R. Johnson, Christopher J. Hillar
- SIAM J. Matrix Analysis Applications
- 2002
The question of whether all words in two real positive definite letters have only positive eigenvalues is addressed and settled (negatively). This question was raised some time ago in connection with… (More)
- Christopher J. Hillar, Darren L. Rhea
- The American Mathematical Monthly
- 2007
Much less known, however, is that there is a description of Aut(G), the automorphism group of G. The first compete characterization that we are aware of is contained in a paper by Ranum [1] near the… (More)
- Christopher J. Hillar, Troels Windfeldt
- J. Comb. Theory, Ser. B
- 2008
The study of graph vertex colorability from an algebraic perspective has introduced novel techniques and algorithms into the field. For instance, it is known that k-colorability of a graph G is… (More)
- Christopher J. Hillar, Friedrich T. Sommer
- IEEE Transactions on Information Theory
- 2015
Sparse coding or sparse dictionary learning has been widely used to recover underlying structure in many kinds of natural data. Here, we provide conditions guaranteeing when this recovery is… (More)
A long-standing conjecture asserts that the polynomial p(t) = Tr[(A + tB)m] has positive coefficients when m is a positive integer and A and B are any two n × n positive definite Hermitian matrices.… (More)
Let K be a totally real number field with Galois closure L. We prove that if f ∈ Q[x1, . . . , xn] is a sum of m squares in K[x1, . . . , xn], then f is a sum of 4m · 2 ([L : Q] + 1 2 ) squares in… (More)
A new algorithm is proposed for a) unsupervised learning of sparse representations from subsampled measurements and b) estimating the parameters required for linearly reconstructing signals from the… (More)
- Christopher J. Hillar, Ram Mehta, Kilian Koepsell
- 2014 IEEE International Conference on Image…
- 2014
The Hopfield network is a well-known model of memory and collective processing in networks of abstract neurons, but it has been dismissed for use in signal processing because of its small pattern… (More)