Permutation Statistical Methods: Calculation Efficiencies

Linear Models: Permutation Methods

Statistical Delay Calculation

This paper discusses a statistical approach to static timing analysis. Delays of gates and wires are modeled by stochastic values instead of the triple best case, typical and worst case delay. This has the advantage of avoiding the overly pessimistic (optimistic) outcome of traditional worst (best) case calculations. The paper proposes a new scheme to perform the delay calculations with stochas...

On the Relative Efficiencies of Gradient Methods

A comparison is made among various gradient methods for maximizing a function, based on a characterization by Crockett and Chernoff of the class of these methods. By defining the "efficiency" of a gradient step in a certain way, it becomes easy to compare the efficiencies of different schemes with that of Newton's method, which can be regarded as a particular gradient scheme. For quadratic func...

Computational Methods in Permutation Patterns

OF THE DISSERTATION Computational Methods in Permutation Patterns by Brian Koichi Nakamura Dissertation Director: Doron Zeilberger Given two permutations σ ∈ Sk and π = π1 . . . πn ∈ Sn, the permutation π is said to contain the pattern σ if there exists 1 ≤ i1 < . . . < ik ≤ n such that πi1 . . . πik is order-isomorphic to σ. Each such subsequence is called an occurrence of σ in π. Over the pas...

A comparison of random field theory and permutation methods for the statistical analysis of MEG data.

We describe the use of random field and permutation methods to detect activation in cortically constrained maps of current density computed from MEG data. The methods are applicable to any inverse imaging method that maps event-related MEG to a coregistered cortical surface. These approaches also extend directly to images computed from event-related EEG data. We determine statistical thresholds...