New PDF release: ASEAN's Cooperative Security Enterprise: Norms and Interests

By H. Katsumata

ISBN-10: 0230229298

ISBN-13: 9780230229297

ASEANs defense Enterprise explores the importance of ASEANs cooperative protection firm the questions of even if and in what feel this company matters.

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Additional info for ASEAN's Cooperative Security Enterprise: Norms and Interests in the ASEAN regional Forum (Critical Studies of the Asian Pacific)

Sample text

4 The Threshold Pool Mix The threshold pool mix is defined by two parameters: the threshold n, and the pool size N . Each round r is defined by collecting a message batch Br of size n such that the contents of the mix are then Sr = (Br ∪ Pr ). The flush set Fr is then selected as random subset of Sr of size n. The messages of Fr are forwarded and the pool for round r + 1 is set to Pr = (Sr − Fr ). The values of n and N are 1 The steady-state strategy was described in [12], and we introduce the term here only as a convenient shorthand.

Let us assume that we choose βN balls at random from set of αN black balls and (1 − α)N white balls without replacing. Let X be the number of black balls chosen. Then for γ > 0 Pr(|X − αβN | > 2βγN) ≤ 2 exp(−γ) . Now we can estimate the values ai /a and bi /b. We use Lemma 3 with the parameters N = n/k, α = ak/n and β = 1/k. We get: Pr ai − a k Pr ai < a k > √ 2γn/k < 2 exp(−γ) . Of course it implies − √ 2γn/k < 2 exp(−γ) . 36 M. Klonowski and M. Kutyłowski So by dividing by a we get Pr ai a < 1 k − √ 2γn ka < 2 exp(−γ) .

Let us assume that we choose βN balls at random from set of αN black balls and (1 − α)N white balls without replacing. Let X be the number of black balls chosen. Then for γ > 0 Pr(|X − αβN | > 2βγN) ≤ 2 exp(−γ) . Now we can estimate the values ai /a and bi /b. We use Lemma 3 with the parameters N = n/k, α = ak/n and β = 1/k. We get: Pr ai − a k Pr ai < a k > √ 2γn/k < 2 exp(−γ) . Of course it implies − √ 2γn/k < 2 exp(−γ) . 36 M. Klonowski and M. Kutyłowski So by dividing by a we get Pr ai a < 1 k − √ 2γn ka < 2 exp(−γ) .

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ASEAN's Cooperative Security Enterprise: Norms and Interests in the ASEAN regional Forum (Critical Studies of the Asian Pacific) by H. Katsumata


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