We define a statistic, called weight, on involutions and consider two applications in which this statistic arises. Let I (n)denote the set of all involutions on [n](= {1, 2, . . . , n}) and let F(2n)denote the set of all fixed point free involutions on [2n]. For an involution δ, let |δ| denote the number of 2-cycles in δ. Let [n]q = 1+q+· · ·+qn−1 and let (k)q denote the q-binomial coefficient....

Student's t-statistic is a data-based linear transformation of an average. This paper proposes an extension i) to more general estimates including m.l.e.'s and M-estimates, and ii) to nonlinear transformations, so that the variance of the estimate is approximately constant. The expansion of the statistic and its properties are derived using basic procedures for the symbolic computation of asymp...

Statistical Rate Monotonic Scheduling (SRMS) is a generalization of the classical RMS results of Liu and Layland [LL73] for periodic tasks with highly variable execution times and statistical QoS requirements. The main tenet of SRMS is that the variability in task resource requirements could be smoothed through aggregation to yield guaranteed QoS. This aggregation is done over time for a given ...

In our discussion of linear models relating rCBF to design factors and gCBF, we have not considered the computational problems of simultaneously fitting the model for thousands of voxels.32 Viewing the problem from a multivariate perspective provides efficient computation, and offers some insight into the problem. In this section we demonstrate the relationship between the simultaneous general ...