My past research interests included differential algebraic equations, nonlinear analysis and relations between symmetries and structural properties.

I recently investigated hierarchical structures, starting from group cohomology, continuing with semi-group theory and ending with lattices and universal algebra.

8h
comment Alternative proofs of Schwartz–Zippel lemma
A short reference to a section in paper without summary, and a remark which you officially claim should have been a comment. Even if somebody would upvote this, do you really think that this is a good way to write an answer?
8h
comment Alternative proofs of Schwartz–Zippel lemma
Can you take a look at lemma 2.2 in web.stanford.edu/~rrwill/graph-cr.pdf? This is what Ryan Williams means by his comment under my answer, and it's on my ToDo list ever since to check whether it can be generalized to commutative rings. It seems to me you are currently much deeper into this than me, so why don't you give it a try?
2d
comment Differential algebra and differential-algebraic equations
@Calle If you speak German, then section 3.2.1 in mod_geom_betr_klas_diffop.pdf gives a good idea for a relation between symmtries and structural properties, i.e. coupling or non-zero structure. Here are visualizations of non-zero structure of DAEs in integral form and non-zero structure of DAEs in semi-explicit form. See "Matrices and Matroids for System Analysis"
Sep
1
answered Differential algebra and differential-algebraic equations
Sep
1
reviewed Close Two versions of arithmetic instructions in RISC. One modifies the flags and the other doesn't
Sep
1
comment Reference for mixed graph acyclicity testing algorithm?
On second thought, it is a bit more complicated, because we need a dynamic digraph representation instead of a static digraph representation, such that deletion of edges can be performed in O(1) time. I know that you are an expert in dynamic graphs, but let me describe one possible solution nevertheless. The lists of incoming and outgoing edges would not just contain the neighbouring vertex, but also point to the identical edge in the opposite list at the neighbouring vertex. But this issue is independent of whether mixed graph representations or digraph representations are used.
Sep
1
comment Reference for mixed graph acyclicity testing algorithm?
Your algorithm can still be implemented to be linear time, even if the graph is represented as a digraph (with lists for the incoming and outgoing directed edges for each vertex). If a vertex has only a single incoming edge left, you remove the corresponding outgoing edge if it is there, and then remember that this step doesn't need to be done again for this vertex.
Sep
1
comment Reference for mixed graph acyclicity testing algorithm?
@DavidEppstein The acyclicity testing itself is done in linear time. But you are right, the time any of those algorithms needs to find the first elementary circuit (of length >=3) is not linear (in the worst case). Worse, most available implementations of Johnson's algorithm seem to use more than O((n+e)(c+1)) time, when applied to a single directed circle (with n vertices, e=n edges, and c=1 elementary cycles). Still, this was intended to be a correct answer, because Johnson's paper seems to be the most quoted reference for "finding elementary circuits".
Aug
31
reviewed Approve suggested edit on What's the difference between Adaptive Control and a Kalman Filter?
Aug
30
revised Reference for mixed graph acyclicity testing algorithm?
deleted 4 characters in body
Aug
30
comment Reference for mixed graph acyclicity testing algorithm?
@DavidEppstein Finding mixed cycles in a mixed graph is equivalent to finding elementary cycles (of length >=3) in the corresponding directed graph. Finding a reference for that statement might be challenging, but proving this statement is straightforward. I now added the statement and its proof to the answer. (Also added a remark without proof that computing the block-cut tree allows to delete every possible vertex that can be deleted without affecting the elementary cycles.)
Aug
30
revised Reference for mixed graph acyclicity testing algorithm?
added a proof of the correspondence between mixed cycles and elementary directed cycles (and added a reference to the block-cut tree)
Aug
30
answered Advanced Differential Geometry Textbook
Aug
30
answered Reference for mixed graph acyclicity testing algorithm?
Aug
29
reviewed No Action Needed Whats Wrong with this LL(1) Grammar?
Aug
29
reviewed Close New computer build shuting down after half second
Aug
29
reviewed Close TrueNorth As a GPU
Aug
29
reviewed Close Can anyone show me computer?
Aug
29
reviewed Close Can you recommend me book with problems?
Aug
29
reviewed Close Difference between "Dedicated Video Memory" and "System Video Memory"
1 2 3 4 5