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acculturalization makes a person out of a human organism. The term personality derives from the Latin persona: an individual carrying out a role (p. 199). The connotation is slightly different from the usual one of mask (Magnavita, 2002). Others have emphasized the importance of the cultural and social system most noteworthy of these, Erik Erickson (1950) in his volume Childhood and Society and the anthropologist, Edward Sapir (Mandelbaum, 1963), who also believed that sociocultural and personality phenomenon are only artificially separated. It is interesting that before his premature death, Sullivan collaborated with Sapir about the cultural contributions he was articulating in his interpersonal theory. Sapir wrote: But we do maintain that such differences of analysis are merely imposed by the nature of the interest of the observer and are not inherent in the phenomenon themselves (p. 546). However, what is remarkable is that most personality theorists still conceived of personality as the processes within the individual, although this would change dramatically with Sullivan s (1953) interpersonal model and Bowen s (1978) triadic model. Arthur Staats (1983) was also a proponent of unification. In his volume Psychology s Crisis of Disunity: Philosophy and Method for a Unified Science, he wrote:



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There are a lot of useful code samples available on the main Arduino site and in the forums where the Arduino community swap code snippets. The RGB LED code additions shown here were adapted from code available there.

(a) A + A' is symmetric. (b) A - A' is skew-symmetric. (c) AA' is symmetric. (d) A' A is symmetric.





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A summary of known leader election protocols Scenario 1 2 3 3 3 3 3 Time slots with probability 1 1/f e ln f log u log f O[(log n)2 + (log f )2] O( f log n) O{min[(log n)2 + (log f )2, f log n]} log log n + o(log log n) + O(log f ) log log n + 2.78 log f + o(log log n + log f ) Time slots, average e O(log u) O[(log n)2] O(log n) O(log n) log log n + o(log log n) log log n + o(log log n)

i,2,0,Dd -1 1 i,2,0,Dd -2 1

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Taking c1 to be the ideal clock, we now de ne the clock of any other arbitrary node i as ci . We de ne ci as ci,t ai (t Di ) Ci (t) where Di is an unknown constant modeling the fact that it is not known when ci is started relative to c1 . ai . 0 is a constant and for each i, ai [ alowbound , aupbound where aupbound , alowbound . 0 are nite. This bound on ai means that the frequency offsets between any two nodes cannot be unbounded. We assume that a known function fa (s) with s [ alowbound , aupbound gives the percentage of nodes with any given a value. Thus, the fraction of nodes with a values in the range s0 to s1 can be found by integrating fa (s) from s0 to s1 . We also assume that j fa (s)j , Ga , for some constant Ga . We keep this function constant as we increase the number of nodes in the network. Ci (t) is a zero mean Gaussian process with samples Ctj N (0, s 2 ), for j [ N, independent and identically distributed. We assume s 2 , 1 and note that s 2 is de ned in terms of the clock of node i. We assume that Ci (t) is Gaussian since the root-mean-square (RMS) jitter is characterized by the Gaussian distribution [34]. Thus, this model assumes that there is a bounded constant frequency offset between the oscillators of any two nodes as well as some random frequency jitter. The reasoning behind the clock model in equation (2.1) comes from the following oscillator model for the instantaneous frequency f (t), f (t) f0 Df fr (t) (2:2) (2:1)

(B) 170 150

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5

symbols are encoded into longer codewords. Suppose that the message probabilities are given in decreasing order, p1 > p2 pm . (a) Prove that for any binary Huffman code, if the most probable message symbol has probability p1 > 2 , that symbol must be 5 assigned a codeword of length 1. (b) Prove that for any binary Huffman code, if the most probable message symbol has probability p1 < 1 , that symbol must be 3 assigned a codeword of length 2. 5.26 Merges. Companies with values W1 , W2 , . . . , Wm are merged as follows. The two least valuable companies are merged, thus forming a list of m 1 companies. The value of the merge is the sum of the values of the two merged companies. This continues until one supercompany remains. Let V equal the sum of the values of the merges. Thus, V represents the total reported dollar volume of the merges. For example, if W = (3, 3, 2, 2), the merges yield (3, 3, 2, 2) (4, 3, 3) (6, 4) (10) and V = 4 + 6 + 10 = 20. (a) Argue that V is the minimum volume achievable by sequences of pairwise merges terminating in one supercompany. (Hint: Compare to Huffman coding.) (b) Let W = Wi , Wi = Wi /W , and show that the minimum merge volume V satis es W H (W) V W H (W) + W. 5.27 (5.147)

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