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3323 Location-Based Key Management A problem with the schemes explained so far is that they do not take the location of sensor nodes after deployment into consideration Even imperfect information about deployment might help to enhance signi cantly the performance of the various schemes This is because, in this case, the scheme can ensure that nodes closer together have a larger number of common keys Nodes which are far away need not have any common keys This can be justi ed due to the fact that direct long-distance communication among nodes would be rare, unnecessary, and also impossible in many scenarios This is the approach taken in [14] The authors assume that information about deployment can be derived from the way the nodes are deployed The authors consider nonuniform sensor deployment and show how it can help to improve the performance of key predistribution The scheme proposed in this paper consists of three phases as for the other random key predistribution schemes earlier, namely key predistribution, shared key discovery, and path-key establishment The last two phases are the same as those considered in the earlier scheme in [15, 16] It is only the rst phase that is considerably different Hence, we focus on explaining only the rst phase here The authors consider that nodes are deployed in groups Consider a possible deployment as shown in Figure 313 Here the nodes are assumed to be deployed in groups around each deployment point shown as a dot Thus, 36 different groups are shown in this gure Some deployment points are shown as points A, B, C, D, E, F, G, H, and I Now, the nodes are grouped into several such groups Further, the global key space pool is also divided into subgroups of key spaces Each subgroup of key spaces is associated with a subgroup of nodes Thus, a key-space subgroup is associated with each deployment point in the gure What is now needed is a scheme that ensures that, when the deployment points of two groups are closer to each other, the amount of overlap.

It is therefore enough to have an asymptotic expansion of (e it 1)/ ( ) of the type (626) so that X is a ltered white noise On the other hand, the FBMs are not elliptic Gaussian random processes of the type de ned earlier, since the lower inequality of ellipticity (632) is not veri ed Moreover, if the symbol depends on t, relation (634) is no longer true and the elliptic Gaussian random processes are no longer ltered white noises Let us reconsider Hypothesis 63 The rst two points are necessary so that the symbol AX behaves asymptotically at high frequency as if it does not depend on t If we want to distinguish the two models roughly, we can consider that elliptic Gaussian random processes have more regular trajectories, whereas ltered white noises lend themselves better to identi cation Consequently, let us reconsider the manner of determining the local regularity of an elliptic Gaussian random process and very brie y summarize the reasoning of [BEN 97b] The starting point for the study of the regularity in the elliptic Gaussian random processes is, as for FBM, a Karhunen-Loeve expansion of the elliptic Gaussian random processes in adapted bases The selected orthonormal base is built starting from the base (613) of L2 ( ) by supposing: = (AX ) 2 ( ) where the fractional power of AX is de ned by means of a symbolic calculation on the operators This leads to: X=

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Perhaps the best way to visualize the steps needed to implement a move to customer-based project management would be to view it as a project As with any good project, a key first step in getting out of the starting gate lies in identifying the necessary steps in implementing the new system Next, we need to consider how we establish a schedule for the change, include significant milestones, key personnel to be involved, and so forth When the change is envisioned as a project, it gives us a working model for moving from the current system to the target model1 Figure 82 shows a simplified work breakdown structure (WBS) as a tool to illustrate some of the important aspects of such a system introduction in your organization We have grouped the key steps in the process along the lines of internal and external analysis, protocol development, testing and refinement, and implementation Like any effective project, the work breakdown structure for creating a customer-based project success program involves several

as and in L2 ( )

(635)

The regularity of X is the consequence of wavelet type estimates which relate to and its rst derivative and which resemble to (616) A precise statement is

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