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More precise information on ECG is provided by multifractal analysis, because their local regularity varies wildly from point to point In the speci c case of RR intervals, several studies have shown that the multifractal spectrum correlates well with the heart condition ([IVA 99, MEY 03, GOL 02]) Roughly speaking, we observe two notable phenomena: On average, the local regularity of healthy RR is smaller than that in presence of, eg, congestive heart failure In other words, pathologies increase the local regularity Healthy RR have much more variability in terms of local regularity; congestive heart failure reduces the range of observed regularities These results may be traced back to the fact that congestive heart failure is associated with profound abnormalities in both the sympathetic and parasympathetic control mechanisms that regulate beat-to-beat variability [GOL 02] A precise view on the mechanisms leading to multifractality is important if we want to understand the purposes it serves and how it will be modi ed in response to external changes or in case of abnormal behavior As of today, there is no satisfactory multifractal model for RR intervals ([AMA 99]) As a preliminary step toward this goal, we shall describe in this section a remarkable feature of the time-evolution of the local regularity Obviously, calculating the time evolution of the local regularity gives far more information than the sole multifractal spectrum Indeed, the latter may be calculated from the former, while the reverse is not true In addition, inspecting the variations of local regularity yields new insights which cannot be deduced from a multifractal spectrum, since all time-dependent information is lost on a spectrum This is crucial for RR intervals, since, as we will see, the evolution of local regularity is strongly (negatively) correlated with the RR signals This fact prompts the development of new models that would account for the fact that, when the RR intervals are larger, the RR signal is more irregular, and vice versa In that view, we shall brie y describe a new mathematical model that goes beyond the usual multifractional Brownian motion (MBM) Recall that the MBM is the following random process, that depends on the functional parameter H(t), where H : [0, ) [a, b] (0, 1) is a C 1 function:.

WH(t) (t) =

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Page 55 following the feedback that we will get However, we have to keep in mind that the pilot project is going to involve our key future project stakeholders, including our customer, and it is important that they get a favorable impression about what we are trying to accomplish At this phase, we cannot afford to lose the credibility of our program The great strength in using the pilot project is that testing the system at the field in its early phase will provide faster and better results than trying to conduct a series of almost infinite fine-tunings from behind the desk We can learn far more from actually observing the project in the field than we ever can hope to know about it from viewing a series of drawings and specifications When beta-testing the project through a PEP, however, it is vital that we pay attention to organizing an efficient system for gathering and utilizing the feedback One of the big mistakes we routinely witness comes from firms who devote enormous resources to the planning of projects and almost nothing to creating a feedback system to allow for organization-wide learning This is a factor that in the end will help us to consolidate the lasting substance of our plan and enable the necessary buy-in from the whole supply chain organization to occur Several good frameworks for the contents of the project execution plan can be found in the project management literature6 Modifying these to fit our intended purpose is often the easiest way of getting started Another way is to compose the elements of the plan without any template by starting from the needs of the particular case There is, however, quite a lot of thinking and cumulative experience incorporated into the standard templates published in the literature by different writers that makes them definitely worth considering Furthermore, these templates include detailed descriptions of the write-ups under the different subtitles, helping the person responsible for composing the document to stay focused This is especially important when incorporating the comments and change proposals that are coming from the different project stakeholders into the main framework Remember that the goal is to.

[(t s)H(t) 1/2 ( s)H(t) 1/2 ]dW (s) (t s)H(t) 1/2 dW (s)

The main feature of MBM is that its H lder exponent may be easily prescribed; at each point t0 , it is equal to H(t0 ) with a probability of one Thus, MBM allows us to describe phenomena whose regularity evolves in time/space For more details on MBM, see 6

Noncollaborative intrusion detection systems are those in which the nodes that are part of the intrusion detection system act individually in performing the various roles associated with detection Thus, such nodes will not only have to collect data but will also have to analyze the collected data themselves This would lead to lower communication overhead amongst the nodes In addition, this is also a less complex approach since each node acts individually An attempt at addressing the question of the role of nodes in a noncollaborative intrusion detection system has been made in [80 83]

Figure 1110 shows two paths of MBM with a linear function H(t) = 02 + 06t and a periodic H(t) = 05 + 03 sin(4 t) We clearly see how regularity evolves over time

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