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This paper describes a Buchberger-style algorithm to compute a Gröbner basis of a polynomial ideal, allowing for a selection strategy based on "signatures". We explain how three recent algorithms can be viewed as different strategies for the new algorithm, and how other selection strategies can be formulated. We describe a fourth as an example. We analyze the strategies both theoretically and empirically, leading to some surprising results.

This paper is a survey on the area of signature-based Gröbner basis algorithms that was initiated by Faugère's F5 algorithm in 2002. We explain the general ideas behind the usage of signatures. We show how to classify the various known variants by 3 different orderings. For this we give translations between different notations and show that besides notations many approaches are just the same. Moreover, we give a general description of how the idea of signatures is quite natural when performing the reduction process using linear algebra. This survey shall help to outline this field of active research. At the moment the area of signature-based Gröbner basis algorithms is confusing and vast. More and more papers are published proving statements already proven before, and even more publications can be found on "new" variants that boil down to be a known one just with a different notation. In this paper we try to give a rigorous survey on signature-based Gröbner basis theory, including all variants known up to now. We lay an emphasis on understanding and we show how the variants presented over the last years are mostly differ in small parts only. Moreover, we give the reader a vocabulary book at hand which helps to understand how notations, varying for different authors, coincide. Since this is a survey, we do not give proofs if they are long, complex, or do not help in understanding the topic. We always explain the idea behind the proofs and refer to the related publication which includes a complete proof. There the reader is then, with our descriptions and explanations, able to understand the

As one of the leading causes of elderly patients’ hospitalisation, proximal femur fractures (PFFs) will present an increasing socioeconomic problem in the near future. This is a result of the demographic change that is expressed by the increasing proportion of elderly people in society. Peri-operative management must be handled attentively to avoid complications and decrease mortality rates. To deal with the exceptional needs of the elderly, the development of orthogeriatric centres to support orthogeriatric co-management is mandatory. Adequate pain medication, balanced fluid management, delirium prevention and the operative treatment choice based on comorbidities, individual demands and biological rather than chronological age, all deserve particular attention to improve patients’ outcomes. The operative management of intertrochanteric and subtrochanteric fractures favours intramedullary nailing. For femoral neck fractures, the Garden classification is used to differentiate between non-displaced and displaced fractures. Osteosynthesis is suitable for biologically young patients with non-dislocated fractures, whereas total hip arthroplasty and hemiarthroplasty are the main options for biologically old patients and displaced fractures. In bedridden patients, osteosynthesis might be an option to establish transferability from bed to chair and the restroom. Postoperatively, the patients benefit from early mobilisation and early geriatric care. During the COVID-19 pandemic, prolonged time until surgery and thus an increased rate of complications took a toll on frail patients with PFFs. This review aims to offer surgical guidelines for the treatment of PFFs in the elderly with a focus on pitfalls and challenges particularly relevant to frail patients.

We introduce the RB algorithm for Gröbner basis computation, a simpler yet equivalent algorithm to F5GEN. RB contains the original unmodified F5 algorithm as a special case, so it is possible to study and understand F5 by considering the simpler RB. We present simple yet complete proofs of this fact and of F5's termination and correctness.RB is parametrized by a rewrite order and it contains many published algorithms as special cases, including SB. We prove that SB is the best possible instantiation of RB in the following sense. Let X be any instantiation of RB (such as F5). Then the S-pairs reduced by SB are always a subset of the S-pairs reduced by X and the basis computed by SB is always a subset of the basis computed by X.

The interest on applying mesenchymal stromal cells (MSCs) in orthopedic disorders has risen tremendously in the last years due to scientific successes in preclinical in vitro and animal model studies. In a wide range of diseases and injuries of the musculoskeletal system, MSCs are currently under evaluation, but so far have found access to clinical use only in few cases. The current assignment is to translate the acquired knowledge into clinical practice. Therefore, this review aims at presenting a synopsis of the up-to-date status of the use of MSCs and MSC related cell products in musculoskeletal indications. Clinical studies were included, whereas preclinical and animal study data not have been considered. Most studies published so far investigate the final outcome applying bone marrow derived MSCs. In fewer trials the use of adipose tissue derived MSCs and allogenic MSCs was investigated in different applications. Although the reported results are equivocal in the current literature, the vast majority of the studies shows a benefit of MSC based therapies depending on the cell sources and the indication in clinical use. In summary, the clinical use of MSCs in patients in orthopedic indications has been found to be safe. Standardized protocols and clear definitions of the mechanisms of action and the mode and timing of application as well as further coordinated research efforts will be necessary for finally adding MSC based therapies in standard operating procedures and guidelines for the clinicians treating orthopedic disorders.

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Objectives-A retrospective analysis of injuries caused by vehicles that were reversing or rolling backwards to establish guidelines for prevention was performed. Patients and methods-Medical records and questionnaires completed by parents for 32 children admitted to the Department of Pediatric Surgery, Graz, within the past eight years, were analysed. Results-The median age was 2.1 years (1.0-14.0 years). Fourteen of 32 of the cars were driven by family members (43.8%); three were rolling backwards without a driver (9.4%). The median injury severity score was 3 (1-27) and the most common injuries were contusions (40.6%), fractures (31.3%), and lacerations/burns (21.9%). Most incidents occurred in driveways (37.5%) or farmyards (21.9%). Altogether 70.3% of children sustained "runover" injuries, 29.6% were hit by the rear bumper or injured by a breaking window. Conclusions-Toddlers playing in driveways or farmyards are at risk of a injury caused by reversing vehicles/vehicles rolling backwards. (Injury Prevention 2001;7:327-328)