In this paper we present a polynomial-time algorithm to solve the following problem: given a non-zero polynomial fe Q[X] in one variable with rational coefficients, find the decomposition of f into irreducible factors in Q[X]. It is well known that this is equivalent to factoring primitive

positive real ffl, a data point p is a (1 + ffl)-approximate nearest neighbor of q if its distance from q is within a factor of (1 + ffl) of the distance to the true nearest neighbor. We show that it is possible to preprocess a set of n points in R d in O(dn log n) time and O(dn) space, so that given a

, and Givens QR factorization. Performance evaluation indicates that locality optimization is especially crucial for scaling up the performance of parallel code.

is difficult, and typical implementations require only 1% to 4% of the number of modular multiplications required by the RSA scheme. Due to their simplicity, security and speed, these schemes are ideally suited for microprocessor-based devices such as smart cards, personal computers, and remote control system.q.

to a publicly specified power e, and then taking the remainder when the result is divided by the publicly specified product, n, of two large secret prime numbers p and q. Decryption is similar; only a different, secret, power d is used, where e · d ≡ 1 (mod (p − 1) · (q − 1)). The security

R factor = 0.052; wR factor = 0.114; data-to-parameter ratio = 18.4. The title compound, [Zn(C8H10F3O2)2(CH4O)2], is a dimethanol coordinated zinc complex with the acetyl acetonate derivative 1,1,1-trifluoro-5,5-dimethylhexane-2,4dionate. The bis--diketonate complex, which is isostructural with its

≪ p, and the zi’s are i.i.d. N(0, σ 2). Is it possible to estimate x reliably based on the noisy data y? To estimate x, we introduce a new estimator—we call the Dantzig selector—which is solution to the ℓ1-regularization problem min ˜x∈R p ‖˜x‖ℓ1 subject to ‖A T r‖ℓ ∞ ≤ (1 + t −1) √ 2 log p · σ

of all points (x ′ , t ′ ) with x ′ ∈ B(x, t, r) and t ′ ∈ [t, t + △t] or t ′ ∈ [t + △t, t], depending on the sign of △t. A ball B(x, t, ǫ −1 r) is called an ǫ-neck, if, after scaling the metric with factor r −2, it is ǫ-close to the standard neck S 2 × I, with the product metric, where S 2 has

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are highly cross-correlated, and principal components analysis implies that they are mostly driven by a single common factor. An important implication of this finding is that if any explanatory variables have been omitted, they are likely not firm-specific. We therefore re-run the regression, but 1 this time