4,269 reputation
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bio website cs.ox.ac.uk/people/…
location Oxford, United Kingdom
age 51
visits member for 4 years, 1 month
seen 5 hours ago

Sep
22
revised nonnegativity conditions for a polynomial in two variables
more references, and an explanation
Sep
22
answered nonnegativity conditions for a polynomial in two variables
Sep
22
comment Complexity of Untwisting Polygons
generating random polygons is a different story then; they care about the uniformity, etc...
Sep
22
comment Complexity of Untwisting Polygons
I'm not sure it's not better to forget all the edges and just construct a polygon directly.
Sep
22
awarded  Custodian
Sep
22
reviewed Close Algorithm to find the “optimal” path in a given graph
Sep
22
reviewed Approve Non-trivial bounds for polynomials at a fixed point
Sep
22
answered Complexity of Untwisting Polygons
Sep
20
reviewed Approve Changing Left Comodules into Right Comodules via the Antipode, and Comodule Tensor Products
Sep
20
comment Fast computation of a Groebner basis - What is Possible
arguably the fastest Groebner bases implementations are www-salsa.lip6.fr/~jcf/Software
Sep
3
comment Is this problem on weighted bipartite graph solvable in polynomial time or it is NP-Complete
Why do you talk about finding a sequence? The order you pick up your $v_i$'s does not matter. Better talk about a subset of A. Do you allow weights to be negative? If not, then you trivially will have to take the whole A.
Sep
3
comment On the positivity of matrices
The vector space of matrices commuting with G has a basis {$I$,$\pi+\pi^4$,$\pi^2+\pi^3$}, where $\pi$ is the permutation matrix corresponding to the cyclic permutation (1,2,3,4,5). Thus $P$ will be a linear combination of these 3 matrices.
Sep
3
comment On the positivity of matrices
$G$ is able to guarantee that $P_{ij}=p$, as the dimension of the centraliser algebra (i.e. the vector space of matrices commuting with every element in $G$) is 3, which can be e.g. checked directly, or by computing the permutation character of $G$. All these things I don't define may be found in books on permutation groups, e.g. P.Cameron's books.google.co.uk/books/about/…
Sep
2
comment On the positivity of matrices
G depends on M only, and can be checked to be of size 10.
Sep
2
comment On the positivity of matrices
One way to conclude that for $P$ being the average over an orbit all these $P_{ij}=p$, would be to note that $P$ commutes with all $\Pi\in G$. One can check that the algebra of all matrices commuting with $G$ coincides with the algebra of symmetric circulant matrices. Thus $P$ has the claimed form.
Sep
2
revised On the positivity of matrices
added a link to the article I referred to
Sep
2
comment On the positivity of matrices
@Hansen: I don't see how you would complete a proof "by hand" without being able to reduce the number of parameters significantly.
Sep
2
comment On the positivity of matrices
here it is: journals.cambridge.org/article_S0305004100036185
Sep
2
awarded  Enlightened
Sep
1
comment On the positivity of matrices
What I am saying is: take an offending P, and average it over G. This gives a symmetric circulant matrix which is still offending, and which only depends on one parameter, $p$.