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C j = log2 |cj j | |c22 | |c11 | k k k We de ne: C j = log2 | j j | | 22 | | 11 | ck ck ck

The exponent f (i) is then given as the result of the linear regression of C j with respect to j Let us observe that if cj = cj , for any k and j, ie, if all the GIFS coef cients k k have their amplitude in ] 1 ; 1[, then we are in the estimation framework of the 2 H lder exponent from the Schauder coef cients sj Indeed, in this case, we have k C j = log2 |sj j | and it is known [TRIE 78] that the Schauder base characterizes the k local regularity of continuous and nowhere differentiable functions (and also more regular functions, under certain conditions [JAF 02b]) We now present some numerical tests on synthetic signals We compare the three methods described earlier (wavelets, Wigner-Ville and GIFS) applied to the generalized Weierstrass functions:

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Figure 415 Tree-authenticated one-way chain (to authenticate a routing update with sequence number 1, metric 1, the shaded values have to be used)

W (t) =

Page 195 alternative does exist We offer another model for running projects; a model that takes as its starting point the belief that the steps we take to develop, manage, and maintain strong customer/contractor relationships will pay huge dividends downstream Making this approach work is not easy It requires a recommitment on the part of the project firm to the principles we all intuitively acknowledge; for example, customer satisfaction is the true determinant of project success It requires us to take these principles and apply them (and sometimes reapply them) to all aspects of our project operations No one remains immune The project engineers serve an important ambassadorial role with the customer just as the project manager or the sales department In other words, the commitment must be total or it will falter Respectively, the new approach requires the customer to appreciate the effort of the project firm toward their total satisfaction Together, a completely new level of communication is needed between the parties to create the trust that is an absolutely fundamental driver for the success of this approach

2 ks(t) sin(2k t)

It is shown in [DAO 98] that its H lder function is W (t) = s(t), under certain conditions on s The choice of these functions is motivated by many reasons: they are simple to synthesize and it is easy to vary W (t); they have already been studied by many authors [GON 92a, TRIC 93] and provide a reliable generic model for different phenomena [JAG 90]; they are synthesized neither from wavelets nor from GIFS, which makes fair comparisons possible Figure 94 (respectively 96) shows the function W (t) on [0; 1] obtained by taking s(t) = t (respectively s(t) = | sin(5 t)|) Figure 95 (respectively 97) shows its H lder function estimation using the methods mentioned earlier, the theoretical curve being represented by a thick line The standard line represents the GIFS estimation, the thin line represents the Schauder base estimation, the dashed line represents the WTMM (Morlet wavelet) estimation Finally, the mixed line represents the time-scale energy distribution (pseudo-Wigner) estimation

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random secret and s is the sequence number The anchor of each hash chain is Hk 1 (X,s) where k is the maximum value of the metric To allow nodes to authenticate these anchors, each node also builds a hash tree using the anchors as leaves as shown in the gure This node then needs to send the root of the hash tree (rightmost node in the gure) to every node in the network authentically This hash tree root is then used to authenticate entries in route updates that have this node as the destination A node that sends a route update to itself with a new sequence number s includes the root of the hash chain H(X,s), the anchor of the hash chain and the path to the root of the hash tree To authenticate the update, another node veri es the anchor for that sequence number by following the path to the root of the hash tree It can then verify the authenticator corresponding to the sequence number and given metric by hashing it a xed number of times and comparing with the anchor of that chain If these tests are validated, such a node can then propagate the route update after updating the metric and the hash value Any other node can repeat the same tests to validate the route updates Thus, any node can verify the authenticator for sequence number s and metric m Note that this approach addresses both the problems given earlier 443 S-DSDV

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