Objectives: Orthopaedic surgeons have a responsibility to minimise risks of ionising radiation to patients, themselves and staff. This study aims to establish the understanding of radiation practice, legislation and risk by orthopaedic surgeons. Methods: A nationwide online survey of UK-based orthopaedic surgeons was conducted. Participants answered eighteen multiple-choice questions assessing level of radiation safety training, basic principles/knowledge of ionising radiation, relevant legislation and operating practice. Results: A total of 406 surgeons completed the survey. 92% reported using intra operative ionising radiation at least once per week. 38% received no formal training on radiation safety. Knowledge of basic principles of radiation and legislation was limited. There was variable knowledge when labelling an image intensifier machine and choosing its safest orientation. Poor uptake of radiation protection equipment was noted. Only 19% agreed they had adequate training in ionising radiation safety and 27% reported receiving adequate training in equipment emitting ionising radiation in the operating theatre. Conclusion: Many orthopaedic surgeons in the UK do not believe they are adequately trained in radiation safety. There is a deficiency amongst practicing surgeons in basic knowledge, relevant legislation and practicalities of the use of ionising radiation in the operating room. This could potentially put patients and healthcare professionals at additional risk. We recommend that a standardised national training programme on the basic principles and safety of ionising radiation is implemented for all practicing orthopaedic surgeons. Advances in knowledge: This paper is the first UK national survey amongst orthopaedic surgeons and is one of the largest reported internationally.
We consider low-space algorithms for the classic E D problem: given an array of n input integers with O(log n) bit-length, decide whether or not all elements are pairwise distinct. Beame, Clifford, and Machmouchi [FOCS 2013] gave an Õ(n 1.5 )-time randomized algorithm for E -D using only O(log n) bits of working space. However, their algorithm assumes a random oracle (in particular, read-only random access to polynomially many random bits), and it was asked as an open question whether this assumption can be removed.In this paper, we positively answer this question by giving an Õ(n 1.5 )-time randomized algorithm using O(log 3 n log log n) bits of space, with one-way access to random bits. As a corollary, we also obtain a poly(n)-space O * (2 0.86n )-time randomized algorithm for the Subset Sum problem, removing the random oracles required in the algorithm of Bansal, Garg, Nederlof, and Vyas [STOC 2017].The main technique underlying our results is a pseudorandom hash family based on iterative restrictions, which can fool the cycle-finding procedure in the algorithms of Beame et al. and Bansal et al.
Given a set of numbers, the k-SUM problem asks for a subset of k numbers that sums to zero. When the numbers are integers, the time and space complexity of k-SUM is generally studied in the word-RAM model; when the numbers are reals, the complexity is studied in the real-RAM model, and space is measured by the number of reals held in memory at any point.We present a time and space efficient deterministic self-reduction for the k-SUM problem which holds for both models, and has many interesting consequences. To illustrate:In general, any polylogarithmic-time improvement over quadratic time for 3-SUM can be converted into an algorithm with an identical time improvement but low space complexity as well. 3-SUM is in deterministic time O(n 2 ) and space O( √ n), derandomizing an algorithm of Wang. A popular conjecture states that 3-SUM requires n 2−o(1) time on the word-RAM. We show that the 3-SUM Conjecture is in fact equivalent to the (seemingly weaker) conjecture that every O(n .51 )-space algorithm for 3-SUM requires at least n 2−o(1) time on the word-RAM. For k ≥ 4, k-SUM is in deterministic O(n k−2+2/k ) time and O( √ n) space.
Posterior tibial tendon subluxation in the setting of an ankle fracture is a rare occurrence and, to our knowledge, has not been reported in the trimalleolar ankle fracture subtype. We report a case of a 24-year-old male who sustained a right, closed trimalleolar ankle fracture and concomitant posterior tibial tendon anterior subluxation after a motor vehicle collision. The posterior tibial tendon was found to be incarcerated in the fracture. He underwent operative treatment to relocate the tendon and for open reduction and internal fixation for his fracture. It is imperative to assess for soft tissue entrapment in foot and ankle injuries as it may impede reduction by closed means and may lead to poor outcomes if not appropriately identified and addressed.
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