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where hk was de ned in Section 2.4.1. Note that the variance of Ti in the timescale of c1 is in the form required by Theorem 2.1. Also, the variance is upper bounded by some constant, since ai is lower bounded by alowbound . Thus, the properties of Ac1 (t) j,1 are characterized by Theorem 2.1. Figure 2.3 illustrates the properties. The result of Theorem 2.1 has signi cant implications for synchronization. First note that since N ! 1, Ac1hk (to ) ! 0, node j sees a zero crossing that occurs at an j, integer value in the time scale of c1 (as N ! 1, we have hk ! 1). Now following our synchronization mechanism outlined in Section 2.4.1, we know that when the R2 nodes start transmitting synchronization pulses, the pulse transmission time (t0 Ti ) for any node i in R2 will satisfy the requirements of Theorem 2.1. This is because node i is in the broadcast domain of node 1, and from earlier in this section we know that its optimal estimate of the next pulse arrival time is a nite-mean Gaussian random variable. Furthermore, the mean is the exact time node 1 increments its operational counter. Thus, we can apply Theorem 2.1 to the transmissions of the R2 nodes and any node l in R2 < R3 will see a received signal Ac1h2 (t1 ) 0 for l, N ! 1, where t1 is the time when node 1 next increments s1 (t). Since a node i in R3 can effectively see the exact time the pulse from node 1 makes a zero-crossing, its

Note: (1) - (6) are standard rules of calculus for functions with vector arguments. For the chain rule see, e.g., Magnus & Neudecker (1988, 5, Sec. 12). (7) and (8) follow from (2). (9) is obtained from standard rult's for derivatives by writing x' Ax in summation notation and computing the derivative for each individual component of x. (10) and (11) follow from (9) and the chain rule (6). (12) is a consequence of the product and chain rules.

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1977, pp 31 32) There is no doubt that ful llment of the James-Lange dream would have been a very pleasant conclusion to the search for speci c emotions But, although the hope remained, it was not to be Dreams die hard To those who still insist on a patterning approach, we are only left with Bertrand Russell s probably apocryphal response to the question of how he would react to being confronted with God after his death: Lord, you did not give us enough evidence! What about an unspeci c relation between viscera and emotion, that is, a general autonomic response Schachter s studies provided one piece of evidence The same physiological antecedent potentiated different emotions It is also the case that widely different emotions show relatively little difference in physiological patterns.

Linear sequential circuits are an important part of convolutional encoders. They are constructed by using basic memory units, or delays, combined with adders and scalar multipliers that operate over GF(q). These linear sequential circuits are also known as nite state sequential machines (FSSMs) [7]. The number of memory units, or delays, de nes the level of memory of a given convolutional code Cconv (n, k, K ), determining also its error-correction capability. Each memory unit is assigned to a corresponding state of the FSSM. Variables in these machines or circuits can be bits, or a vector of bits understood as an element of a eld, group or ring over which the FSSM is de ned [9 15]. In these algebraic structures there is usually a binary representation of the elements that adopt the form of a vector of components taken from GF(2). FSSM analysis is usually performed by means of a rational transfer function G(D) = P(D)/Q(D) of polynomial expressions in the D domain, called the delay domain, where message and code sequences adopt the polynomial form M(D) and C(D), respectively. For multiple input multiple output FSSMs, the relationship between the message sequences and the code sequences is described by a rational transfer function matrix G(D). A convolutional encoder is basically a structure created using FSSMs that for a given input sequence generates a given output sequence. The set of all the code sequences constitutes the convolutional code Cconv .

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