Orthogonalities and functional equations

In this survey we show how various notions of orthogonality appear in the theory of functional equations. After introducing some orthogonality relations, we give examples of functional equations postulated for orthogonal vectors only. We show their solutions as well as some applications. Then we discuss the problem of stability of some of them considering various aspects of the problem. In the sequel, we mention the orthogonality equation and the problem of preserving orthogonality. Last, but not least, in addition to presenting results, we state some open problems concerning these topics. Taking into account the big amount of results concerning functional equations postulated for orthogonal vectors which have appeared in the literature during the last decades, we restrict ourselves to the most classical equations

Risk profiles and one-year outcomes of patients with newly diagnosed atrial fibrillation in India: Insights from the GARFIELD-AF Registry.

BACKGROUND: The Global Anticoagulant Registry in the FIELD-Atrial Fibrillation (GARFIELD-AF) is an ongoing prospective noninterventional registry, which is providing important information on the baseline characteristics, treatment patterns, and 1-year outcomes in patients with newly diagnosed non-valvular atrial fibrillation (NVAF). This report describes data from Indian patients recruited in this registry. METHODS AND RESULTS: A total of 52,014 patients with newly diagnosed AF were enrolled globally; of these, 1388 patients were recruited from 26 sites within India (2012-2016). In India, the mean age was 65.8 years at diagnosis of NVAF. Hypertension was the most prevalent risk factor for AF, present in 68.5% of patients from India and in 76.3% of patients globally (P < 0.001). Diabetes and coronary artery disease (CAD) were prevalent in 36.2% and 28.1% of patients as compared with global prevalence of 22.2% and 21.6%, respectively (P < 0.001 for both). Antiplatelet therapy was the most common antithrombotic treatment in India. With increasing stroke risk, however, patients were more likely to receive oral anticoagulant therapy [mainly vitamin K antagonist (VKA)], but average international normalized ratio (INR) was lower among Indian patients [median INR value 1.6 (interquartile range {IQR}: 1.3-2.3) versus 2.3 (IQR 1.8-2.8) (P < 0.001)]. Compared with other countries, patients from India had markedly higher rates of all-cause mortality [7.68 per 100 person-years (95% confidence interval 6.32-9.35) vs 4.34 (4.16-4.53), P < 0.0001], while rates of stroke/systemic embolism and major bleeding were lower after 1 year of follow-up. CONCLUSION: Compared to previously published registries from India, the GARFIELD-AF registry describes clinical profiles and outcomes in Indian patients with AF of a different etiology. The registry data show that compared to the rest of the world, Indian AF patients are younger in age and have more diabetes and CAD. Patients with a higher stroke risk are more likely to receive anticoagulation therapy with VKA but are underdosed compared with the global average in the GARFIELD-AF. CLINICAL TRIAL REGISTRATION-URL: http://www.clinicaltrials.gov. Unique identifier: NCT01090362

Trichloroethylene: An Invisible Cause of Parkinson's Disease?

The etiologies of Parkinson's disease (PD) remain unclear. Some, such as certain genetic mutations and head trauma, are widely known or easily identified. However, these causes or risk factors do not account for the majority of cases. Other, less visible factors must be at play. Among these is a widely used industrial solvent and common environmental contaminant little recognized for its likely role in PD: trichloroethylene (TCE). TCE is a simple, six-atom molecule that can decaffeinate coffee, degrease metal parts, and dry clean clothes. The colorless chemical was first linked to parkinsonism in 1969. Since then, four case studies involving eight individuals have linked occupational exposure to TCE to PD. In addition, a small epidemiological study found that occupational or hobby exposure to the solvent was associated with a 500% increased risk of developing PD. In multiple animal studies, the chemical reproduces the pathological features of PD.Exposure is not confined to those who work with the chemical. TCE pollutes outdoor air, taints groundwater, and contaminates indoor air. The molecule, like radon, evaporates from underlying soil and groundwater and enters homes, workplaces, or schools, often undetected. Despite widespread contamination and increasing industrial, commercial, and military use, clinical investigations of TCE and PD have been limited. Here, through a literature review and seven illustrative cases, we postulate that this ubiquitous chemical is contributing to the global rise of PD and that TCE is one of its invisible and highly preventable causes. Further research is now necessary to examine this hypothesis

KRAS mutational status impacts pathologic response to pre-hepatectomy chemotherapy: a study from the International Genetic Consortium for Liver Metastases

Background: A major response to pre-hepatectomy chemotherapy has been associated with improved survival in patients who undergo resection of colorectal liver metastases (CRLM). However, the role of tumor biology, as exemplified by overall and codon-specific KRAS mutational status, in predicting response to chemotherapy is not well defined. Methods: Pathologic response was characterized as minor or major depending on the percentage of remnant viable cells (&gt;50% vs &lt;50%, respectively). Multivariable logistic regression was used to identify factors associated with major response. Results: 319 patients met inclusion criteria. 229 patients had a KRAS wild-type (wtKRAS) tumor and 90 harbored KRAS mutations (mutKRAS). A major pathologic response was more commonly noted in patients with wtKRAS compared to mutKRAS (48.5% vs 33.3%, P = 0.01) and wtKRAS status remained independently associated with a major response (P = 0.04). On a codon-specific level, major pathologic response occurred less frequently in those with codon 13 mutations (17.7%) compared to those with codon 12 (35.4%), and other KRAS mutations (33.3%). Importantly, codon 13 mutations were independently associated with minor pathologic response (P = 0.023). Conclusions: Patients with wtKRAS tumors appear to have the highest likelihood of experiencing a major response after preoperative chemotherapy. Future studies in “all-comer” cohorts are needed to confirm these findings and further investigate the response of codon 13 mutations. © 2019 International Hepato-Pancreato-Biliary Association Inc

Natural variation of toxicity in encrusting sponge Crambe crambe (Schmidt) in relation to size and environment

The presence of intraspecific variation in toxicity and its relationship with biological or ecological factors were studied in the spongeCrambe crambe. Within-specimen (periphery and central part), between-size (10,000 mm2) and between-habitat (well-illuminated and dark communities) variations in toxicity were evaluated by the Microtox bioassay. Quantitative differences were detected that were not attributable to within-specimen variation but to size and habitat effects. Habitat comparisons showed that sponges in the shaded habitat were significantly more toxic than those of the well-illuminated community. Sponges of the smaller size classes displayed significantly less toxicity than the medium-sized specimens. Results are interpreted under the optimal defense theory and their ecological implications are considered.Peer reviewe