Symmetries of weight enumerators and applications to Reed-Muller codes

Gleason's 1970 theorem on weight enumerators of self-dual codes has played a crucial role for research in coding theory during the last four decades. Plenty of generalizations have been proved but, to our knowledge, they are all based on the symmetries given by MacWilliams' identities. This paper is intended to be a first step towards a more general investigation of symmetries of weight enumerators. We list the possible groups of symmetries, dealing both with the finite and infinite case, we develop a new algorithm to compute the group of symmetries of a given weight enumerator and apply these methods to the family of Reed-Muller codes, giving, in the binary case, an analogue of Gleason's theorem for all parameters.Comment: 14 pages. Improved and extended version of arXiv:1511.00803. To appear in Advances in Mathematics of Communication

The trace field of hyperbolic gluings

The first part of the thesis focuses on the study of the adjoint trace field of hyperbolic manifolds, an algebraic invariant introduced by Vinberg and generalizing the invariant trace field of dimension 3. We compute the adjoint trace field in the case of general hyperbolic gluings, and show how it can be used to prove that certain gluings are nonarithmetic. In the second part we introduce and motivate the concept of pseudo-arithmeticity, a notion that encompasses all known examples of hyperbolic manifolds. We then prove that gluings of arithmetic pieces are always pseudo-arithmetic, using results from the first part

Type 2 diabetes mellitus and osteoarthritis

Objectives: Type 2 diabetes mellitus (T2DM) and osteoarthritis (OA) are common diseases that frequently co-exist, along with overweight/obesity. While the mechanical impact of excess body weight on joints may explain lower limb OA, we sought to explore whether T2DM is linked to OA outside of excess weight and whether T2DM may play a role in OA pathophysiology. The consequence of T2DM on OA outcomes is a question of research interest. Methods: We conducted a critical review of the literature to explore the association between T2DM and OA, whether any association is site-specific for OA, and whether the presence of T2DM impacts on OA outcomes. We also reviewed the literature to assess the safety of anti-OA treatments in patients with T2DM. Results: T2DM has a pathogenic effect on OA through 2 major pathways involving oxidative stress and low-grade chronic inflammation resulting from chronic hyperglycemia and insulin resistance. T2DM is a risk factor for OA progression and has a negative impact on arthroplasty outcomes. Evidence is mounting for safety concerns with some of the most frequently prescribed anti-OA medications, including paracetamol, non-steroidal anti-inflammatory drugs, and corticosteroid injections, while other anti-OA medications may be safely prescribed in OA patients with T2DM, such as glucosamine and intra-articular hyaluronic acid. Conclusions: Future research is needed to better understand whether diabetes control and prevention can modulate OA occurrence and progression. The selection of therapy to treat OA symptoms in patients with T2DM may require careful consideration of the evidence based to avoid untoward safety issues.The meeting was funded by the ESCEO, a Belgian not-for-profit organization. The authors thank the Chair for Biomarkers of Chronic Diseases and the International Scientific Partnership Program (ISPP#0111) at King Saud University, Riyadh, Saudi Arabia for their suppor

Correction to: Is There Enough Evidence for Osteosarcopenic Obesity as a Distinct Entity? A Critical Literature Review

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Mainstreaming life cycle thinking through a consistent approach to footprints

Over recent years, footprints have emerged as an important means of reporting environmental performance. Some individual footprints have become quite sophisticated in their calculation procedures. However, as an overallclass of environmental metrics they have been poorly defined, having a variety of conceptual foundations and an unclear relationship to LCA. The variety and sometimes contradictory approaches to quantification have also led to confusing and contradictory messages in the marketplace which have undermined their acceptance by industry and governments.In response, a task force operating under the auspices of the UNEP/SETAC Life Cycle Initiative project on environmental Life Cycle Impact Assessment has been working to develop generic guidance for developers of footprint metrics. The initial work involved forming a consensual position on the difference between footprints and existing LCA impact category indicators. In short, footprints are deemed to have a primary orientation toward society and nontechnical stakeholders and report only on selected topics of concern. On the other hand, LCA impact category indicators have a primary orientation toward technical stakeholders and report in relation to a larger framework designed for comprehensive evaluation of environmental performance and trade-offs. The task force has also developed a universal footprint definition. In parallel to Area of Protection, we introduce Area of Concern. In the same way that LCA uses impact category indicators to assess impacts that follow a common cause-effect pathway toward Areas of rotection, ootprint metrics address Areas of Concern. The critical difference is that Areas of Concern are defined by the interests of stakeholders in society rather than the LCA community. In addition, Areas of Concern are stand-alone and not part of a framework intended for comprehensive environmental performance assessment. Accordingly, footprints are universally defined as metrics used to report life cycle assessment results addressing an Area of Concern