Home
Articles
Research
Teaching
Problems
Code
Expository

Selected Code

Retinal Image Coding Model

Coming Soon!

Efficient Hopfield network learning

You'll want to get Python, Numpy, SciPy, and MatplotLib, all conveniently contained in this distribution Anaconda (free).

Hopfield network Python class with fitting using minimum probability flow learning:

Fingerprints example

(with Jascha Sohl-Dickstein and Kilian Koepsell) Efficient and optimal binary Little-Hopfield associative memory storage using minimum probability flow, 2011, NIPS (DISCML Workshop), 2012. pdf | arxiv.

(with Jascha Sohl-Dickstein and Kilian Koepsell) Novel local learning rule for neural adaptation fits Hopfield memory networks efficiently and optimally, BMC Neuroscience, vol. 14, no. Suppl 1, pp. P215, 2013. (Cosyne Conference 2013).

Most tensor problems are NP-hard

The following code verifies Example 1.5 and Lemma 7.1 in the following paper:

(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



Solvability of symmetric word equations

The following Macaulay 2 code computes the table found in the paper:

(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 

bar

Solvability of symmetric word equations

The following Maple code computes Jacobians (and subspace restrictions of Jacobians) for Words in matrix letters. You will need to "right-click save as" download these files (as your browser might think they are readable).

maple code 1 | maple code 2

The first code listed above verified a calculation that showed that there are word equations in positive definite letters with multiple postiive definite solutions. This settled an open conjecture. The second piece of code gives evidence for the conjecture that in the 2-by-2 case, there is always a unique solution. These results can be found in the paper:

(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

Algebraic Characterization of Uniquely Colorable Graphs

The following Singular code verifies a counterexample to a conjecture of Xu discovered by Akbari, Mirrokni, and Sadjad.

singular code

It uses Groebner basis techniques to discover unique colorability of graphs. The details can be found in the following paper:

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

Introduction to Maple

A basic introduction to Maple (there is some code here). pdf







 

















Home | Articles | Research | Teaching | Problems | Expository