Modified repeated median filters

We discuss moving window techniques for fast extraction of a signal comprising monotonic trends and abrupt shifts from a noisy time series with irrelevant spikes. Running medians remove spikes and preserve shifts, but they deteriorate in trend periods. Modified trimmed mean filters use a robust scale estimate such as the median absolute deviation about the median (MAD) to select an adaptive amount of trimming. Application of robust regression, particularly of the repeated median, has been suggested for improving upon the median in trend periods. We combine these ideas and construct modified filters based on the repeated median offering better shift preservation. All these filters are compared w.r.t. fundamental analytical properties and in basic data situations. An algorithm for the update of the MAD running in time O(log n) for window width n is presented as well. --signal extraction,robust filtering,drifts,jumps,outliers,computational geometry,update algorithm

Data structures

We discuss data structures and their methods of analysis. In particular, we treat the unweighted and weighted dictionary problem, self-organizing data structures, persistent data structures, the union-find-split problem, priority queues, the nearest common ancestor problem, the selection and merging problem, and dynamization techniques. The methods of analysis are worst, average and amortized case

Techniques for Constructing Efficient Lock-free Data Structures

Building a library of concurrent data structures is an essential way to simplify the difficult task of developing concurrent software. Lock-free data structures, in which processes can help one another to complete operations, offer the following progress guarantee: If processes take infinitely many steps, then infinitely many operations are performed. Handcrafted lock-free data structures can be very efficient, but are notoriously difficult to implement. We introduce numerous tools that support the development of efficient lock-free data structures, and especially trees.Comment: PhD thesis, Univ Toronto (2017

Emergency Operations Methodology for Extreme Winter Storm Events

Winter storms have increased in frequency and intensity since the 1950s, and average annual precipitation is projected to continue to increase across the northern United States. In response to these trends, many states have developed, or are interested in developing, emergency-response plans for extreme winter storm events. This report provides a series of six emergency response plan case studies as well as a synthesis of best practices related to emergency-response planning for extreme winter weather. It is intended to provide a blueprint for transportation agencies seeking to develop or improve their own extreme winter weather emergency-response plans, including how to coordinate an effective response across multiple agencies and jurisdictions

Discontinuous Galerkin finite element method with anisotropic local grid refinement for inviscid compressible flows

A new discretization method for the three-dimensional Euler equations of gas dynamics is presented, which is based on the discontinuous Galerkin finite element method. Special attention is paid to an efficient implementation of the discontinuous Galerkin method that minimizes the number of flux calculations, which is generally the most expensive part of the algorithm. In addition a detailed discussion of the truncation error of the presented algorithm is given. The discretization of the Euler equations is combined with anisotropic grid refinement of an unstructured, hexahedron-type grid to achieve optimal resolution in areas with shocks, vortices, and other localized flow phenomena. The data structure and searching algorithms necessary for efficient calculation on highly irregular grids obtained with local grid refinement are discussed in detail. The method is demonstrated with calculations of the supersonic flow over a 10? ramp and the ONERA M6 wing under transsonic flow condition

Bulk updates and cache sensitivity in search trees

This thesis examines two topics related to binary search trees: cache-sensitive memory layouts and AVL-tree bulk-update operations. Bulk updates are also applied to adaptive sorting. Cache-sensitive data structures are tailored to the hardware caches in modern computers. The thesis presents a method for adding cache-sensitivity to binary search trees without changing the rebalancing strategy. Cache-sensitivity is maintained using worst-case constant-time operations executed when the tree changes. The thesis presents experiments performed on AVL trees and red-black trees, including a comparison with cache-sensitive B-trees. Next, the thesis examines bulk insertion and bulk deletion in AVL trees. Bulk insertion inserts several keys in one operation. The number of rotations used by AVL-tree bulk insertion is shown to be worst-case logarithmic in the number of inserted keys, if they go to the same location in the tree. Bulk deletion deletes an interval of keys. When amortized over a sequence of bulk deletions, each deletion requires a number of rotations that is logarithmic in the number of deleted keys. The search cost and total rebalancing complexity of inserting or deleting keys from several locations in the tree are also analyzed. Experiments show that the algorithms work efficiently with randomly generated input data. Adaptive sorting algorithms are efficient when the input is nearly sorted according to some measure of presortedness. The thesis presents an AVL-tree-based variation of the adaptive sorting algorithm known as local insertion sort. Bulk insertion is applied by extracting consecutive ascending or descending keys from the input to be sorted. A variant that does not require a special bulk-insertion algorithm is also given. Experiments show that applying bulk insertion considerably reduces the number of comparisons and time needed to sort nearly sorted sequences. The algorithms are also compared with various other adaptive and non-adaptive sorting algorithms