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Now, using (9.13) we obtain E[Z] = n + 2 ln f + o(n + ln f ) and, therefore, g(n) = 2n + 4 ln f + o(n + ln f ). It follows that, for every f 1, with probability at least 1 1/f , the partition tree has at most 2n + 4 ln f + o(n + ln f ) internal nodes. Further, it is well known that a full binary tree with N internal nodes has exactly N + 1 leaf nodes. Therefore, with probability exceeding 1 1/f , the partition tree has 4n + 8 ln f + o(n + ln f ) nodes. Consequently, we have proved the following result. Theorem 5.2 Even if n is not known beforehand, a single-hop, single-channel, n station radio network with CD can be initialized, with probability exceeding 1 1/f , for every f 1, in 4n + 8 ln f + o(n + ln f ) time slots. 9.5.3 Protocol for Unknown n: The No-CD Case Suppose that the stations in a subset P transmit on the channel. If the stations can detect collisions, then every station can determine whether |P | = 0, |P | = 1, or |P | 2. On the other hand, if the stations lack the collision detection capability, then they can only determine whether |P | = 1 or |P | 1. Next, we show that once a leader is elected, the RN with no-CD can simulate one time

Figure 15.2. Schematics of cell-based bioreactor designs. The majority of liver cell-based bioreactor designs fall into these four general categories, each with inherent advantages and disadvantages, reviewed extensively in Allen et al. [2001].

is derived in a similar way: (dii dw ) 2 . (n 1) (25.79)

It is well known that the TS fuzzy system can be represented as a neural network (Jang, 1993). The network-like structure enables the exibility and parallelism and the development of effective learning techniques. The con uence of neural networks as structure framework with the power of fuzzy systems as knowledge granule models leads to neuro-fuzzy constructs. eTS can also be represented as a six-layer neuro-fuzzy system (Figure 2.2), which is similar to the fuzzy basis-function networks (Wang & Mendel, 1992). The rst layer takes the inputs, xk and feeds the second layer, which has neurons with activation functions determined by the membership functions mij xk de ned in (2.2). In this way, the second layer acts as the granulation of the input universes. The third layer

(1993) concluded that individuals who perceive work relationships with supervisors and coworkers as nonsupportive and high in con ict appear to be at increased risk for minor illnesses and physical symptoms (eg, headache, fatigue) Therefore, the quality and function of work relationships appear to play a role in women s health Still, gender differences have been reported in the effect of workplace support on health and well-being In an investigation of the amount and effects of social support, job stress, and tedium experienced by men and women (Geller & Hobfoll, 1994), women reported greater life tedium than men, and men reported the receipt of more household assistance than women Despite the fact that the men and women in this study reported receiving similar amounts of support from their coworkers and supervisors, men bene ted more from these support sources, particularly coworker support.

The quotation that I have cited above might at rst seem to be a rather grand one surely there are some things that can work without communication But I have thought long and hard about these words, as I m sure Marc Hauser must have done before he committed them to paper, and my conclusion is that if we take a broad de nition of communication as being the sharing of something between A and B some form of communication is essential in the smooth functioning of all things.

To elaborate, suppose we measure the typical distance between the observations we make and c with the sum of squared differences: ( X i c) 2 The least squares principle is to choose as a measure of location the value c that minimizes this sum and leads to c = X , the sample mean But if the typical distance |X i c| instead, minimizing this sum is measured with results in c = M , the sample median That is, different measures of location are obtained depending on how distance is measured Rather than use squared error or absolute error, M-estimators use other measures of error that result in measures of location with good properties under normality as well as when sampling from skewed or heavy-tailed distributions.