Heterotrophic ossification post total knee arthroplasty in a patient with rheumatoid arthritis: a case report

Even though minor degrees of heterotrophic ossification are common in total knee arthroplasty, it is of little clinical significance. But severe degrees of heterotrophic ossification are very rare after total knee arthroplasty. Here we discuss about a 70 years old woman who initially had excellent post-operative range of movements after cemented total knee arthroplasty, but later presented with knee pain, swelling and loss of range of movements after 3 months. X ray showed severe heterotrophic ossification around knee near the quadriceps tendon. She was treated conservatively with non-steroidal anti inflammatory drugs and physiotherapy. After a period of 3 months of physiotherapy, patient regained the lost range of movements and is currently under follow up for the past 1 year. Hence this case instantiates that even in cases of severe Heterotrophic Ossification after total knee arthroplasty, non-operative treatments such as physiotherapy with anti-inflammatory drugs should be the primary option to treat the stiffness before considering surgery.

Range Shortest Unique Substring queries

Let be a string of length n and be the substring of starting at position i and ending at position j. A substring of is a repeat if it occurs more than once in; otherwise, it is a unique substring of. Repeats and unique substrings are of great interest in computational biology and in information retrieval. Given string as input, the Shortest Unique Substring problem is to find a shortest substring of that does not occur elsewhere in. In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over answering the following type of online queries efficiently. Given a range, return a shortest substring of with exactly one occurrence in. We present an -word data structure with query time, where is the word size. Our construction is based on a non-trivial reduction allowing us to apply a recently introduced optimal geometric data structure [Chan et al. ICALP 2018]

Longest Common Prefixes with kk-Errors and Applications

Although real-world text datasets, such as DNA sequences, are far from being uniformly random, average-case string searching algorithms perform significantly better than worst-case ones in most applications of interest. In this paper, we study the problem of computing the longest prefix of each suffix of a given string of length $n$ over a constant-sized alphabet that occurs elsewhere in the string with $k$-errors. This problem has already been studied under the Hamming distance model. Our first result is an improvement upon the state-of-the-art average-case time complexity for non-constant $k$ and using only linear space under the Hamming distance model. Notably, we show that our technique can be extended to the edit distance model with the same time and space complexities. Specifically, our algorithms run in $\mathcal{O}(n \log^k n \log \log n)$ time on average using $\mathcal{O}(n)$ space. We show that our technique is applicable to several algorithmic problems in computational biology and elsewhere

Suffix-prefix queries on a dictionary

In the all-pairs suffix-prefix (APSP) problem, we are given a dictionary R of k strings, S1, . . ., Sk, of total length n, and we are asked to find the length SPLi,j of the longest string that is both a suffix of Si and a prefix of Sj, for all i, j ∈ [1, k]. APSP is a classic problem in string algorithms with many applications in bioinformatics. When all strings of the dictionary are over an integer alphabet of size σ ≤ nO(1), APSP can be solved in the optimal O(n + k2) time with the use of the generalized suffix tree of the dictionary [Gusfield et al., Inf. Process. Lett. 1992]. In many bioinformatics applications, such as in sequence assembly, the size k of dictionary R is very large. In particular, k2 usually dominates n, and thus the k2 factor is the bottleneck both in the time and in the space complexity of such applications. We thus initiate a holistic study on several data structure variants of APSP. In particular, we consider the following types of queries: One-to-One(i, j): output SPLi,j. One-to-All(i): output SPLi,j for every j ∈ [1, k]. Report(i, ℓ): output all distinct j ∈ [1, k] such that SPLi,j ≥ ℓ, where ℓ ≥ 0 is an integer. Count(i, ℓ): output the number of distinct j ∈ [1, k] such that SPLi,j ≥ ℓ, where ℓ ≥ 0 is an integer. Top(i, K): output K distinct j ∈ [1, k] with the highest values of SPLi,j breaking ties arbitrarily. We assume the standard word RAM model of computation with word size w = Ω(log n) and an integer alphabet of size σ ≤ nO(1). We show the following upper bounds: Query Space (words) Query time Note One-to-One(i, j) O(n) O(log log k) Theorem 11 One-to-All(i) O(n) O(k) Theorem 14 Report(i, ℓ) O(n) O(log n/log log n + output) Theorem 19(i) Count(i, ℓ) O(n) O(log n/log log n) Theorem 19(ii) Top(i, K) O(n) O(log2 n/log log n + K) Theorem 22 We also present efficient algorithms for constructing these data structures

Efficient data structures for range shortest unique substring queries†

Let T[1, n] be a string of length n and T[i, j] be the substring of T starting at position i and ending at position j. A substring T[i, j] of T is a repeat if it occurs more than once in T; otherwise, it is a unique substring of T. Repeats and unique substrings are of great interest in computational biology and information retrieval. Given string T as input, the Shortest Unique Substring problem is to find a shortest substring of T that does not occur elsewhere in T. In this paper, we introduce the range variant of this problem, which we call the Range Shortest Unique Substring problem. The task is to construct a data structure over T answering the following type of online queries efficiently. Given a range [α, β], return a shortest substring T[i, j] of T with exactly one occurrence in [α, β]. We present an O(n log n)-word data structure with O(logw n) query time, where w = Ω(log n) is the word size. Our construction is based on a non-trivial reduction allowing for us to apply a recently introduced optimal geometric data structure [Chan et al., ICALP 2018]. Additionally, we present an O(n)-word data structure with O(√ n logɛ n) query time, where ɛ > 0 is an arbitrarily small constant. The latter data structure relies heavily on another geometric data structure [Nekrich and Navarro, SWAT 2012]