Methods and Algorithms for Robust Filtering

We discuss filtering procedures for robust extraction of a signal from noisy time series. Moving averages and running medians are standard methods for this, but they have shortcomings when large spikes (outliers) respectively trends occur. Modified trimmed means and linear median hybrid filters combine advantages of both approaches, but they do not completely overcome the difficulties. Improvements can be achieved by using robust regression methods, which work even in real time because of increased computational power and faster algorithms. Extending recent work we present filters for robust online signal extraction and discuss their merits for preserving trends, abrupt shifts and extremes and for the removal of spikes

Arthroscopic Knotless Modified McLaughlin Procedure for Reverse Hill–Sachs Lesions

Posterior shoulder dislocations often are associated with an impression fracture involving the anterior humeral head known as a reverse Hill–Sachs lesion. These injuries can result in significant bone defects that require surgical management to prevent them from engaging the posterior glenoid. We present a modified arthroscopic, knotless McLaughlin procedure (tenodesis of the subscapularis tendon into the bone defect) for the treatment of small-to medium-sized, engaging Hill–Sachs lesions. The knotless fashion aims to eliminate potential problems associated with knot tying, such as knot migration, knot impingement, and chondral abrasion

Detecting High-Order Interactions of Single Nucleotide Polymorphisms Using Genetic Programming

Motivation: Not individual single nucleotide polymorphisms (SNPs), but high-order interactions of SNPs are assumed to be responsible for complex diseases such as can-cer. Therefore, one of the major goals of genetic association studies concerned with such genotype data is the identification of these high-order interactions. This search is ad-ditionally impeded by the fact that these interactions often are only explanatory for a relatively small subgroup of patients. Most of the feature selection methods proposed in the literature, unfortunately, fail at this task, since they can either only identify individ-ual variables or interactions of a low order, or try to find rules that are explanatory for a high percentage of the observations. In this paper, we present a procedure based on genetic programming and multi-valued logic that enables the identification of high-order interactions of categorical variables such as SNPs. This method called GPAS (Genetic Programming for Association Studies) cannot only be used for feature selection, but can also be employed for discrimination. Results: In an application to the genotype data from the GENICA study, an associa-tion study concerned with sporadic breast cancer, GPAS is able to identify high-order interactions of SNPs leading to a considerably increased breast cancer risk for different subsets of patients that are not found by other feature selection methods. As an applica-tion to a subset of the HapMap data shows, GPAS is not restricted to association studies comprising several ten SNPs, but can also be employed to analyze whole-genome data. Availability: Software is available on request from the authors. Contact

Global non-smooth optimization in robust multivariate regression

Robust regression in statistics leads to challenging optimization problems. Here, we study one such problem, in which the objective is non-smooth, non-convex and expensive to calculate. We study the numerical performance of several derivative-free optimization algorithms with the aim of computing robust multivariate estimators. Our experiences demonstrate that the existing algorithms often fail to deliver optimal solutions. We introduce three new methods that use Powell\u27s derivative-free algorithm. The proposed methods are reliable and can be used when processing very large data sets containing outliers.<br /