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We study of the connection between operator valued central limits for monotone, Boolean and free probability theory, which we shall call the arcsine, Bernoulli and semicircle distributions, respectively. In scalar-valued non-commutative probability these measures are known to satisfy certain arithmetic relations with respect to Boolean and free convolutions. We show that generally the corresponding operator-valued distributions satisfy the same relations only when we consider them in the fully matricial sense introduced by Voiculescu. In addition, we provide a combinatorial description in terms of moments of the operator valued arcsine distribution and we show that its reciprocal Cauchy transform satisfies a version of the Abel equation similar to the one satisfied in the scalar-valued case.

A 16-year-old man was hospitalised with a painful space-occupying lesion in his posterior neck involving muscles, soft tissues, C1 cervical vertebra and vital cervical blood vessels. The true-cut biopsy showed inflammatory tissue. The microbiological analysis, which combined classical bacteriological and molecular methods, yielded at least four different anaerobic species. The patient was treated successfully with a prolonged course of ceftriaxone and metronidazole.

Ischiofemoral impingement (IFI) has been described in the medical literature as a cause of hip pain. IFI occurs due to an abnormal contact or reduced space between the lesser trochanter and the lateral border of the ischium and is an often unrecognised cause of pain and snapping in the hip. Association of multiple exostoses and a skeletal dysplasia characterised by an abnormal modelling of bone metaphysis and osseous deformities is highly characteristic of this disease. Consequently, multiple exostoses may narrow the ischiofemoral space and cause impingement and pain, even in the absence of malignant transformation. Surgical excision of exostosis of the lesser trochanter is a safe and effective method of treatment for patients with IFI. We present a case of left hip pain with incidental finding of hereditary multiple osteochondroma causing IFI and discuss the predisposing factors and review of literature.

Poor sleep impedes children's cognitive, emotional, and psychosocial development. Pediatric sleep dysregulation is common, and children who live in communities of low socioeconomic status experience additional risk factors for short sleep duration and poor sleep quality. School-based training in mindfulness and yoga-informed practices can improve children's behavior and well-being, but effects on objectively measured sleep are unknown.Effects of a school-based health and mindfulness curriculum, which taught practices such as paced breathing, on sleep and stress were examined in 115 children (49 girls, ages 8 to 11 at baseline). Fifty-eight children in a community of low socioeconomic status received the curriculum twice weekly for 2 years. Fifty-seven children in a socioeconomic status-matched community engaged in their usual physical education class instead. In-home ambulatory polysomnography and perceived social stress were measured in all children at 3 time points: at baseline (ie, prior to curriculum exposure) and at 2 yearly follow-ups.Children receiving the curriculum gained an average of 74 minutes of total sleep time, and 24 minutes of rapid eye movement sleep, per night over the 2-year study period. Children not receiving the curriculum experienced a decrease in total sleep time averaging 64 minutes per night, with no changes in rapid eye movement sleep. Sleep improved within the first 3 months of curriculum exposure, in a dose-dependent fashion. Higher curriculum engagement (eg, using the breathing exercises outside of class) was associated with larger gains in total and rapid eye movement sleep duration. Aggregate within-group changes in social stress were not significant. However, among children receiving the curriculum, those who experienced larger gains in total and rapid eye movement sleep duration also experienced larger increases in perceived social stress.A school-based health and mindfulness curriculum improved children's objectively measured sleep over 2 years. Social stress did not mediate these effects; instead, mindfulness training may have increased awareness of environmental stressors, while developing tools to reduce stress vulnerability.Chick CF, Singh A, Anker LA, et al. A school-based health and mindfulness curriculum improves children's objectively measured sleep: a prospective observational cohort study.

There is a recent proliferation of clinical studies about the minimally invasive scarless thyroid surgery. The transoral endoscopic thyroidectomy vestibular approach (TOETVA) carries a great potential for being scarless surgery via a short dissection flap. However, TOETVA has limitations in extracting larger thyroid tumours via the transoral vestibular incision and due to its potential damage to the branches of the mental nerve. The rapidly evolving surgical innovations have now introduced transoral and submental thyroidectomy (TOaST) approach that allows extraction of large thyroid tumours with less flap dissection and minimal postoperative pain. We present a 39-year-old man with a large multinodular goitre. The patient was euthyroid with moderate to severe compression symptoms of difficulty in breathing and swallowing. We performed a TOaST procedure using intraoperative neuromonitoring and indocyanin green fluorescence imaging with an uneventful recovery. This is a first case report from the middle east region that will pave the way to large clinical trials to determine the efficacy and safety of TOaST.

A 42-year-old diabetic man presented to the hospital with severe sepsis and multiorgan dysfunction. A probable respiratory source of sepsis was suspected because of suggestive clinical and radiological findings. He was critically ill and was therefore admitted to intensive care for further management including ventilatory support and renal replacement therapy. He was also found to have marked anaemia requiring multiple blood transfusions with clinical and laboratory evidence pointing towards severe haemolysis. Further workup for the aetiology of pneumonia established a diagnosis of Legionella by confirmatory tests namely legionella antigen in the urine and exponentially rising serum antibody titres. The cause for the severe haemolysis was found to be complement-mediated autoimmune haemolysis as determined by direct antiglobulin test positive for complement components C3 and negative for IgG. Such clinically significant autoimmune haemolysis as a presenting feature, rather than a late complication, has never before been reported in the literature.

We consider a general queueing model with a Poisson arrival process whose rate is random, and realized once for the entire process. We show that the distribution of the arrival rate at arrival instants is the size-biased counterpart of the original distribution. In particular, the ASTA (arrivals see time averages) property does not hold but rather a rate-biased version of it that we define and coin by the term RASTA (Rate-biased ASTA). We show that the RASTA phenomenon plays a crucial role in the analysis of strategic behavior of customers who evaluate the consequences of the actions they take upon arrival. We study such a system with a single server and strategic customers who decide whether to join or balk without observing the queue.

This paper is part of an ongoing endeavor to bring the theory of fair division closer to practice by handling requirements from real-life applications. We focus on two requirements originating from the division of land estates: (1) each agent should receive a plot of a usable geometric shape, and (2) plots of different agents must be physically separated. With these requirements, the classic fairness notion of \emph{proportionality} is impractical, since it may be impossible to attain any multiplicative approximation of it. In contrast, the \emph{ordinal maximin share approximation}, introduced by Budish in 2011, provides meaningful fairness guarantees. We prove upper and lower bounds on achievable maximin share guarantees when the usable shapes are squares, fat rectangles, or arbitrary axis-aligned rectangles, and explore the algorithmic and query complexity of finding fair partitions in this setting. Our work makes use of tools and concepts from computational geometry such as independent sets of rectangles and guillotine partitions. Appears in the 30th International Joint Conference on Artificial Intelligence (IJCAI), 2021

Emergency Medical Services (EMS) in Israel was called on to vaccinate the most vulnerable population—the elderly in assisted living facilities and their caregivers. Two parameters led the operation: (1) maximum use of the scarce COVID-19 vaccine, and (2) minimizing the time it took to reach this entire population. We present the process of vaccinating 126 245 people in two weeks at 756 locations countrywide, focusing on the planning and logistics of this operation. Resilience, flexible logistics, and dedicated personnel provided an efficient public health operation.

A 14-year-old girl, a rear seat passenger on a jet-ski not wearing suitable protective gear, was ‘jumping’ waves at a low velocity when she was ejected backwards off the vehicle, suffering a complex and unusual hydrostatic perineal injury as a result of the high-pressure water stream propelling the jet-ski. She presented to the emergency room with rectal bleeding and perineal and abdominal pain. Initial investigations revealed signs of anorectal injury and both intraperitoneal and extraperitoneal free air and fluid, suggesting a possible rectal perforation. Proctoscopy confirmed the primary diagnosis and exploratory laparotomy revealed an intraperitoneal tear in the rectal wall. The tear was repaired, and protective loop colostomy was performed. Initial results of anal manometry, transrectal ultrasound and anal electromyography were unfavourable. However, 17 months after pelvic floor physiotherapy and biofeedback, the colostomy was reversed, and her continence has returned to her normal (preinjury) state.