Related papers: BPP is in NP and coNP
We give a number theoretic proof of the integrality of certain BPS invariants of knots. The formulas for these numbers are sums involving binomial coefficients and the M\"obius function. We also prove a conjecture about further divisibility…
The paper has been withdrawn due to a crucial error in section 3.
This paper has been withdrawn, because I have merged it with paper I of the series, math.AG/0312190. The main results of this paper now appear in sections 7-9 of the revised version of math.AG/0312190, with shortened and improved proofs.
We present completeness results for inference in Bayesian networks with respect to two different parameterizations, namely the number of variables and the topological vertex separation number. For this we introduce the parameterized…
This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…
This paper has been withdrawn temporarily.
The paper has been withdrawn by the author due to unhappy mistake in the initial scope of the work.
This paper has been withdrawn by the author due to errors.
This paper has been withdrawn by the author due to a gap in the proof of the main result.
We have observed a gap in one of the arguments in the main theorem. We choose to withdraw the paper until we rectify the gap.
This paper has been withdrawn by the author due to a crucial error in one of equation in (3).
This paper has been withdrawn due to non-clearness of some technical points, as well as lack of a reasonable statement of quantization conjecture.
There is a technical issue in the analysis that is not easily fixable. We, therefore, withdraw the submission. Sorry for the inconvenience.
This paper has been withdrawn.
This paper addresses biquadratic polynomial programming (BPP), an NP-hard optimization problem closely related to biquadratic tensors. We first establish several necessary and sufficient conditions for the positive semi-definiteness and…
This paper is withdrawn. The revised paper appears in chao-dyn/9904020
This paper has been withdrawn by the author due to incomplete interpretation for the results.
The paper has been withdrawn
This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.
We construct a reduction which proves that the fooling set number and the determinantal rank of a Boolean matrix are NP-hard to compute.