Posterior dislocation of the hip

Analysis of 55 posterior dislocations of the hip after trauma are presented with some reference to aetiology, and particular reference to management and complications. The results compared favourably with reported large series from abroad. Some suggestions ore made as a result of our experience, which may help to improve the mnagement of this condition.S. Afr. Med. J., 48, 1029 (1974)

Longest common substring made fully dynamic

Given two strings S and T, each of length at most n, the longest common substring (LCS) problem is to find a longest substring common to S and T. This is a classical problem in computer science with an O(n)-time solution. In the fully dynamic setting, edit operations are allowed in either of the two strings, and the problem is to find an LCS after each edit. We present the first solution to this problem requiring sublinear time in n per edit operation. In particular, we show how to find an LCS after each edit operation in Õ(n2/3) time, after Õ(n)-time and space preprocessing. 1 This line of research has been recently initiated in a somewhat restricted dynamic variant by Amir et al. [SPIRE 2017]. More specifically, they presented an Õ(n)-sized data structure that returns an LCS of the two strings after a single edit operation (that is reverted afterwards) in Õ(1) time. At CPM 2018, three papers (Abedin et al., Funakoshi et al., and Urabe et al.) studied analogously restricted dynamic variants of problems on strings. We show that the techniques we develop can be applied to obtain fully dynamic algorithms for all of these variants. The only previously known sublinear-time dynamic algorithms for problems on strings were for maintaining a dynamic collection of strings for comparison queries and for pattern matching, with the most recent advances made by Gawrychowski et al. [SODA 2018] and by Clifford et al. [STACS 2018]. As an intermediate problem we consider computing the solution for a string with a given set of k edits, which leads us, in particular, to answering internal queries on a string. The input to such a query is specified by a substring (or substrings) of a given string. Data structures for answering internal string queries that were proposed by Kociumaka et al. [SODA 2015] and by Gagie et al. [CCCG 2013] are used, along with new ones, based on ingredients such as the suffix tree, heavy-path decomposition, orthogonal range queries, difference covers, and string periodicity

Dynamic and Internal Longest Common Substring

Given two strings S and T, each of length at most n, the longest common substring (LCS) problem is to find a longest substring common to S and T. This is a classical problem in computer science with an O(n) -time solution. In the fully dynamic setting, edit operations are allowed in either of the two strings, and the problem is to find an LCS after each edit. We present the first solution to the fully dynamic LCS problem requiring sublinear time in n per edit operation. In particular, we show how to find an LCS after each edit operation in O~ (n2 / 3) time, after O~ (n) -time and space preprocessing. This line of research has been recently initiated in a somewhat restricted dynamic variant by Amir et al. [SPIRE 2017]. More specifically, the authors presented an O~ (n) -sized data structure that returns an LCS of the two strings after a single edit operation (that is reverted afterwards) in O~ (1) time. At CPM 2018, three papers (Abedin et al., Funakoshi et al., and Urabe et al.) studied analogously restricted dynamic variants of problems on strings; specifically, computing the longest palindrome and the Lyndon factorization of a string after a single edit operation. We develop dynamic sublinear-time algorithms for both of these problems as well. We also consider internal LCS queries, that is, queries in which we are to return an LCS of a pair of substrings of S and T. We show that answering such queries is hard in general and propose efficient data structures for several restricted cases

Alphabet Dependence in Parameterized Matching

The classical pattern matching paradigm is that of seeking occurrences of one string in another, where both strings are drawn from an alphabet set \Sigma. A recently introduced model is that of parameterized pattern matching; the main motivation for this scheme lies in software maintenance where programs are considered "identical " even if variables are different. Strings, under this model, additionally have symbols from a variable set \Pi and occurrences of one string in the other up to a renaming of the variables are sought. In this paper we show that finding the occurrences of a m-length string in a n- length string under the parameterized pattern matching paradigm can be done in time O(n log ß), where ß = min(m; j\Pij); that is, independent of j\Sigmaj. Additionally, we show that in general this dependence on j\Pij is inherent to any algorithm for this problem in the comparison model -- that is, our algorithm is optimal

Alphabet Dependence in Parameterized Matching

The classical pattern matching paradigm is that of seeking occurrences of one string in another, where both strings are drawn from an alphabet set ∑. A recently introduced model is that of parameterized pattern matching; the main motivation for this scheme lies in software maintenance where programs are considered "identical" even if variables are different. Strings, under this model, additionally have symbols from a variable set Π and occurrences of one string in the other up to a renaming of the variables are sought. In this paper we show that finding the occurrences of a m-length string in a n-length string under the parameterized pattern matching paradigm can be done in time O (n log π), where π = min (m, ∣Π∣); that is , independent of ∣∑∣. Additionally, we show that in general this dependence on ∣Π∣ is inherent to any algorithm for this problem in the comparison model – that is, our algorithm is optimal

Analyzing High-Dimensional Data by Subspace Validity

We are proposing a novel method that makes it possible to analyze high dimensional data with arbitrary shaped projected clusters and high noise levels. At the core of our method lies the idea of subspace validity. We map the data in a way that allows us to test the quality of subspaces using statistical tests. Experimental results, both on synthetic and real data sets, demonstrate the potential of our method

Shape-Embedded-Histograms for Visual Data Mining

Scatterplots are widely used in exploratory data analysis and class visualization. The advantages of scatterplots are that they are easy to understand and allow the user to draw conclusions about the attributes which span the projection screen. Unfortunately, scatterplots have the overplotting problem which is especially critical when high-dimensional data are mapped to low-dimensional visualizations. Overplotting makes it hard to detect the structure in the data, such as dependencies or areas of high density. In this paper we show that by extending the concept of Pixel Validity (1) the problem of overplotting or occlusion can be avoided and (2) the user has the possibility to see information about an additional third variable. In our extension of the Pixel Validity concept, we summarize the data which are projected onto a given region by generating a histogram over the required attribute. This is then embedded in the visualization by a pixel-based technique