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The simulation results showing the dependences of the median failure time on the normalized width W=D50 for 20 lines with L 50 mm subjected to a direct current of J 1 MA/cm2 at T 200 C are shown in Fig. 5.3.3. For the upper curve (with squares), D50 3 mm and s 0:5; for the middle curve (with circles), D50 2 mm and s 0:5; and for the lower curve (with triangles), D50 1 mm and s 0:5. All curves indicate a minimum at about W=D50 1, which is in agreement with the observations of Kinsbron [126].

The algorithm is randomized, and in order to meet the two goals with probability at least 1 , for a user-speci ed probability of failure (0, 1), it maintains a sample with expected size 2 1 log( 1 1 ) = 2t Note that the space is independent of the stream length n The sample S is a set of pairs of the form (x, fe (x)) In order to handle potentially unbounded streams, the sampling rate r is not xed, but is adjusted so that the probability 1/r of sampling a stream item decreases as more and more items are considered Initially, S is empty and r = 1 For each stream item x, if x S, then fe (x) is increased by 1.

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abnormalities were not seen in the clinical studies An important side-effect is hypertension, probably caused by the slight adrenergic effect of sibutramine (Lean, 1997) With a dosage of 15 mg daily the diastolic blood pressure rises with an average of 2 mmHg In a higher dosage (60 mg daily) uoxetine can reduce appetite In at least one study uoxetine was shown, as compared to placebo, to give an additional weight loss of 36 kg, but other studies have failed to demonstrate the effect of uoxetine on body weight (Wise, 1992) Fluoxetine is not registered for the treatment of obesity Another approach to achieving weight loss is to in uence the absorption of nutrients in the gastrointestinal tract and so to reduce the daily energy intake Paraf n, for example, has been tried for a long time; a more recent development is the non-absorbent fat-substitute R R R Olean .

Otherwise, x is sampled with rate r, that is, with probability 1/r: if x is sampled, the pair (x, 1) is added to S, otherwise we ignore x and move to the next stream item After sampling with rate r = 1 the rst 2t items, the sampling rate increases geometrically as follows: the next 2t items are sampled with rate r = 2, the next 4t items with rate r = 4, the next 8t items with rate r = 8, and so on Whenever the sampling rate changes, the estimated frequencies of sample items are adjusted so as to keep them consistent with the new sampling rate: for each (x, fe (x)) S, we repeatedly toss an unbiased coin until the coin toss is successful, decreasing fe (x) by 1 for each unsuccessful toss.

The backup GUS must employ a different algorithm for calculating the range residual. Since the backup GUS is not transmitting to the satellite, the WMS cannot model the clock drift at the backup GUS, and therefore an a0 term is not present in the WAAS Type 9 message. In lieu of the a0 term provided by the WMS, the backup GUS calculates an equivalent a0 parameter. The range residual a0 tk for the backup GUS is calculated as follows [44]: a0 tk where BRE RWMS c S tk

We evict (x, fe (x)) from S if fe (x) becomes 0 during this process Effectively, after each sampling rate doubling, S is transformed to exactly the state it would have been in, if the new rate had been used from the beginning Upon a frequency items query, the algorithm returns all sample items whose estimated frequency is at least ( )n The following technical lemma will be useful in the analysis of sticky sampling Although pretty straightforward, we report the proof for the sake of completeness Lemma 1 Let r 2 and let n be the number of stream items considered when the sampling rate is r Then 1/r t/n, where t = 1 log( 1 1 ) Proof It can be easily proved by induction on r that n = rt at the beginning of the phase in which sampling rate r is used.

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