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Dougherty, L M, Abe, J, & Izard, C E (1996) Differential emotions theory and emotional development in adulthood and later life In C Magai & S H McFadden (Eds), Handbook of emotion, adult development, and aging (pp 27 38) San Diego, CA: Academic Press Eccles, J, Adler, T E, Futterman, R, Goff, S B, Kaczala, C M, Meece, J L, et al (1983) Expectancies, values, and academic behaviors In J T Spence (Ed), Achievement and achievement motivation (pp 75 146) San Francisco: Freeman Frey, K S, & Ruble, D N (1990) Strategies for comparative evaluation: Maintaining a sense of competence across the life span In R Sternberg & J Kolligian (Eds), Competence considered (pp 167 189) New Haven, CT: Yale University Press Fung, H H, Rice, C, & Carstensen, L L (2005).

Reactive and proactive motivational changes across adulthood In W Greve, K Rothermund, & D Wentura (Eds), The adaptive.

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Matrix B is known as the matrix of scalar products. As we know from equation 0 (9.20), we can write B in terms of X. Call X(n 1)xm the matrix X where each of the Xi0 0 is shifted to have its origin at X0 : Xi Xi X0 . Then, using equations (9.20) and (9.21), X 0 X 0T B We can solve for X 0 by taking an eigen decomposition of B into an orthonormal matrix of eigenvectors and a diagonal matrix of matching eigenvalues: B X 0 X 0T UVU T X 0 UV 1=2 (9:22)

The cost, however, is that the base station has to precompute the CDM messages in the reverse order That is, in order to include H(CDMi 1 ) in CDMi , the base station has to have CDMi 1 , which implies that it also needs CDMi 2 , and so on Therefore, the base station needs to compute both the high-level and the lowlevel key chains completely to get the commitments of these key chains, and construct all the CDM messages in the reverse order before distributing the rst one of them (Note that the base station only needs to compute the high-level key chain but not all the low-level ones during initialization The base station can delay the computation of a low-level key chain until it needs to distribute the commitment of that key chain) This imposes additional computation during the initialization phase.

Therefore, Codd suggested some other useful, but nonessential ways to think about relations he called one of these the array representation of relations [Codd70] In this representation, we create a table (not a database table, but a textual one a rectangle with gridlines dividing it into smaller cells) with each column representing the corresponding domain from the order de ned in the relation Each row in the table represents an n-tuple from the relation, with no duplicate rows allowed The rows are unordered, but the column order is signi cant, because it is possible for the same domain to be used more than once in the same relation In order to make this even.

Assume that all the key chains have 1000 keys The base station needs to perform about 1,001,000 pseudorandom function operations to generate all the key chain commitments, and 1000 pseudorandom function operations and 1000 MAC operations to generate all the CDM messages Due to the ef ciency of pseudorandom functions, such computation is still practical if the base station is relatively resourceful For example, using MD5 as the pseudorandom function, a modern personal digital assistant (PDA) can nish the preceding computation in several seconds Moreover, the base station does not have to save the low-level key chains Indeed, to reduce the storage overhead, the base station may compute a low-level key chain (again) when the key chain is needed Thus, the base station only needs to store the high-level key chain and the MACs of all the CDM messages.

Further assume both the authentication key and the image of a pseudorandom function are 8 bytes To continue the earlier example, the base station needs (8 8) 1000 16,000 bytes to store the highlevel key chain and the MACs The immediate authentication of CDMi depends on the successful receipt of CDMi 1 However, if a sensor node cannot receive an authentic CDMi due to communication failure or an attacker s active disruption, the sensor node has to fall back to the DOS-tolerant multilevel mTESLA This implies that the base station still needs to distribute CDM messages multiple times in a random manner Now let us assess how dif cult it is for a sensor node to recover if it fails to receive an authentic CDM message We assume an attacker will launch a DOS attack to deter this recovery.