Magnetoencephalography (MEG) is a well-known technique in the presurgical evaluation of epilepsy patients. Like EEG, it can detect and localize epileptic activity. Epilepsy surgery can be used to evaluate MEG source localizations. Resection volumes were determined in 33 epilepsy surgery patients. The resection volume, taken together with the post-operative outcome, was used to evaluate MEG results. The scattering MEG localizations of interictal epileptic activity were represented by an ellipsoidal volume. Using this MEG results ellipsoid, it was demonstrated that a high coverage by the resection volume and a small distance to the resection volume are both correlated to a favourable outcome; in addition, a homogeneous distribution of MEG localizations is correlated to a favourable outcome. This study shows that MEG source localization can help to delineate epileptic activity and, along with other techniques, should be taken into account for epilepsy surgery.

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In many modern applications of queueing theory, the classical assumption of exponentially decaying service distributions does not apply. In particular, Internet and insurance risk problems may involve heavy-tailed distributions. A difficulty with heavy-tailed distributions is that they may not have closed-form, analytic Laplace transforms. This makes numerical methods, which use the Laplace transform, challenging. In this paper, we develop a method for approximating Laplace transforms. Using the approximation, we give algorithms to compute the steady state probability distribution of the waiting time of an M/G/1 queue to a desired accuracy. We give several numerical examples, and we validate the approximation with known results where possible or with simulations otherwise. We also give convergence proofs for the methods.

Internet traffic flows have often been characterized as having power-tailed (long-tailed, fattailed, heavy-tailed) packet interarrival times or service requirements. In this work, we focus on the development of complete and computationally efficient steady-state solutions of queues with power-tailed interarrival times when the service times are assumed exponential. The classical method for obtaining the steady-state probabilities and delay-time distributions for the G/M/1 (G/M/c) queue requires solving a rootfinding problem involving the Laplace-Stieltjes transform of the interarrival-time distribution function. Then the exponential service assumption is combined with the derived geometric arrival-point probabilities to get both the limiting general-time state and delay distributions. However, in situations where there is a power tail, the interarrival transform is typically quite complicated and never analytically tractable. In addition, it is possible that there is only a degenerate steady-state system-size probability distribution. Thus, an alternative approach to obtaining a steady-state solution is typically needed when power-tailed interarrivals are present. We exploit the exponentiality of the steady-state delay distributions for the G/M/1 and G/M/c queues, using level crossings and a transform-approximation method, to develop an alternative rootfinding problem when there are power-tailed interarrival times. Extensive computational results are given.