There is a deep connection between permutations and trees. Certain sub-structures of permutations, called sub-permutations, bijectively map to sub-trees of binary increasing trees. This opens a powerful tool set to study enumerative and probabilistic properties of sub-permutations and to investigate the relationships between ’local’ and ’global’ features using the concept of pattern avoidance. ...

We present a convergence theory for pattern search methods for solving bound constrained nonlinear programs. The analysis relies on the abstract structure of pattern search methods and an understanding of how the pattern interacts with the bound constraints. This analysis makes it possible to develop pattern search methods for bound constrained problems while only slightly restricting the flexi...

In block motion estimation, a search pattern with a different shape or size has a very important impact on search speed and distortion performance. A square-shaped search pattern is commonly adopted in many popular fast algorithms. Recently, a diamond-shaped search pattern was introduced in fast block motion estimation, which has exhibited faster search speed. Based on an in-depth examination o...

The problem of spurious apparent patterns arising by chance is a fundamental one for pattern detection. Classical approaches, based on adjustments such as the Bonferroni procedure, are arguably not appropriate in a data mining context. Instead, methods based on the false discovery rate the proportion of flagged patterns which do not represent an underlying reality may be more relevant. We descr...

The need for pattern discovery in long time series data led researchers to develop algorithms for similarity search. Most of the literature about time series focuses on algorithms that index time series and bring the data into the main storage, thus providing fast information retrieval on large time series. This paper reviews the state of the art in visualizing time series, and focuses on techn...

We extend pattern search methods to linearly constrained minimization. We develop a general class of feasible point pattern search algorithms and prove global convergence to a KarushKuhn-Tucker point. As in the case of unconstrained minimization, pattern search methods for linearly constrained problems accomplish this without explicit recourse to the gradient or the directional derivative of th...

We introduce an abstract definition of pattern search methods for solving nonlinear unconstrained optimization problems. Our definition unifies an important collection of optimization methods that neither compute nor explicitly approximate derivatives. We exploit our characterization of pattern search methods to establish a global convergence theory that does not enforce a notion of sufficient ...

We examine the local convergence properties of pattern search methods, complementing the previously established global convergence properties for this class of algorithms. We show that the step-length control parameter which appears in the definition of pattern search algorithms provides a reliable asymptotic measure of first-order stationarity. This gives an analytical justification for a trad...