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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)

With the destination movie active in Flash, choose File > Open As Library. Select the source movie in the Open As Library dialog box and click Open. Drag an asset from the source movie library onto the Stage or into the library of the destination movie.

(B) 170 150

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)

This translates to an MT template rather like this one:

The MT class (and descendants) provide a log method that is used to store records in the application s log table. These records can be viewed through the MT web interface using the View Activity Log link from MT s main menu. To store log records, use the log routine in the main MT package:

The approach for online learning with the integration of online rule base simpli cation and reduction procedures allows implementing the concept of online transparent modeling in order to improve interpretability and reduce the complexity of fuzzy models acquired with a purely data-driven approach. The behavior of the approach is strongly in uenced by two prede ned parameters: the radius of the clusters (radii) and the similarity threshold between fuzzy sets. Parameter radii can be used to control the number of fuzzy rules, and inherently model complexity and precision, while the similarity threshold parameter can be used to balance the interpretability and numerical accuracy of the model. These two parameters together allow the control of model interpretability, complexity, and precision.

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from (13.102) and (13.103). We now de ne random variables U , V such that Pr(U = l, V = s) = ls . Thus, EU =