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than traditional wavelet thresholding (we should however recall that hard and soft thresholding were not designed for stochastic signals) In particular, this method preserves a roughly correct regularity along the path, while wavelet thresholding yields a signal with both too smooth and too irregular regions Second, it appears that using the degenerate information provided by the at spectrum does not signi cantly decrease the denoising quality 11465 Denoising of road pro les An important problem in road engineering is to understand the mechanisms of friction between rubber and the road This is a dif cult problem, since friction depends on many parameters: the type of rubber, the type of road, the speed, etc Several authors have shown that most road pro les are fractal [RAD 94, HEI 97, GUG 98] on given ranges of scales Such a property has obvious consequences on friction, some of which have been investigated for instance in [RAD 94, KLU 00] The main idea is that, in the presence of fractal roads, all irregularity scales contribute to friction [DO 01]

In [LEG 04a], it is veri ed that road pro les nely sampled using tactile and laser sensors are indeed fractals More precisely, it is shown that they have well-de ned correlation exponents and regularization dimensions over a wide range of scales However, various classes of pro les which have different friction coef cients are not discriminated by these global fractal parameters This means that friction may have relatively low correlation with fractional dimensions or correlation exponents In contrast, experiments show that the pointwise H lder exponent allows us to separate road pro les which have different friction coef cients The laser acquisition system developed at LCPC (Laboratoire central des ponts et chauss es), based on an Imagine optics sensor, allows us to obtain (at the nest resolution) road pro les with a sampling step of 25 microns These signals are very noisy As a consequence, when they are used for computing a theoretical friction ([DO 01]), a very low correlation with the real friction (048) is obtained Since local regularity is related to friction, it seems natural to use one of the regularity-based denoising methods presented above in this case It appears that a Bayesian denoising is well tted; after this denoising, the correlation between theoretical real friction increases up to 086 (see Figure 118) For more on this topic, see [LEG 04b]

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The next key question is related to the number of nodes that need to be part of the intrusion detection architecture as well as the role of each If our goal is to detect all the attacks for all possible mobility scenarios, it is likely that all nodes in the system will have to be part of the intrusion detection process because there is always a possibility that a malicious node A will be directly connected to a single node B, which is the only node with direct visibility to the behavior of the malicious node In order to detect node A s malicious behavior, node B will either need to have the ability to analyze A s behavior or will need to have a sensor that collects suf cient evidence and then sends the evidence to some other node C for further analysis Requiring every node to participate in the intrusion detection process may not be desirable, however, due to inef ciencies associated with this approach It is also likely that in practice it will not be possible to require that all nodes devote resources to the intrusion detection process given the resource constraints and the need for the node to execute other applications Sensor networks are good examples of networks with nodes that have severe resource constraints and most likely cannot support IDS running on each node in the network If we are willing to tolerate less than 100 percent detection accuracy, which is probably the case in a lot of applications, it may not be necessary to run IDS on each node If we can utilize only a subset of the total number of nodes in the intrusion detection process, it is important to decide what role each node needs to play in the intrusion detection process There is no general answer to this question that is well suited for all situations The answer depends on several parameters, such as:.

Defining mission and objectives Identifying the contents and format of the plan Writing the instructions of how to compose the plan Developing the document control procedure for the plan Organizing the training Consolidating the procedure as a part of the QA system of our company

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