Full-Rank Factorization and Moore-Penrose’s Inverse

C. MacDuffee apparently was the first to point out, in private communications, that a full-rank factorization of a matrix A leads to an explicit formula for its Moore-Penrose’s inverse A+. Here we apply this idea of MacDuffee and the Singular Value Decomposition to construct A+

On The Gould’s Formula for Stirling Numbers of The Second Kind

We present an alternative deduction of the Gould’s relation for Stirling numbers of the second kind. Our approach is based in the Nörlund polynomials and in the duality property between the Stirling numbers

Identities of Choi-Lee-Srivastava involving the Euler-Mascheroni’s constant

We give an elementary deduction of the Choi-Lee-Srivastava’s identities involving the Euler Mascheroni’s constant, thus from them is immediate the identity of Wilf

Lanczos Potential for The Weyl Tensor

For arbitrary spacetimes with Petrov types O, N and III, we indicate general results about the  Lanczos potential for the corresponding Weyl tensor

Effectiveness of a cognitive behavioral intervention in patients with medically unexplained symptoms: cluster randomized trial

BACKGROUND: Medically unexplained symptoms are an important mental health problem in primary care and generate a high cost in health services.Cognitive behavioral therapy and psychodynamic therapy have proven effective in these patients. However, there are few studies on the effectiveness of psychosocial interventions by primary health care. The project aims to determine whether a cognitive-behavioral group intervention in patients with medically unexplained symptoms, is more effective than routine clinical practice to improve the quality of life measured by the SF-12 questionary at 12 month. METHODS/DESIGN: This study involves a community based cluster randomized trial in primary healthcare centres in Madrid (Spain). The number of patients required is 242 (121 in each arm), all between 18 and 65 of age with medically unexplained symptoms that had seeked medical attention in primary care at least 10 times during the previous year. The main outcome variable is the quality of life measured by the SF-12 questionnaire on Mental Healthcare. Secondary outcome variables include number of consultations, number of drug (prescriptions) and number of days of sick leave together with other prognosis and descriptive variables. Main effectiveness will be analyzed by comparing the percentage of patients that improve at least 4 points on the SF-12 questionnaire between intervention and control groups at 12 months. All statistical tests will be performed with intention to treat. Logistic regression with random effects will be used to adjust for prognostic factors. Confounding factors or factors that might alter the effect recorded will be taken into account in this analysis. DISCUSSION: This study aims to provide more insight to address medically unexplained symptoms, highly prevalent in primary care, from a quantitative methodology. It involves intervention group conducted by previously trained nursing staff to diminish the progression to the chronicity of the symptoms, improve quality of life, and reduce frequency of medical consultations. TRIAL REGISTRATION: The trial was registered with ClinicalTrials.gov, number NCT01484223 [http://ClinicalTrials.gov].S

Effect of the Mediterranean diet on blood pressure in the PREDIMED trial: results from a randomized controlled trial

BackgroundHypertension can be prevented by adopting healthy dietary patterns. Our aim was to assess the 4-year effect on blood pressure (BP) control of a randomized feeding trial promoting the traditional Mediterranean dietary pattern.MethodsThe PREDIMED primary prevention trial is a randomized, single-blinded, controlled trial conducted in Spanish primary healthcare centers. We recruited 7,447 men (aged 55 to 80 years) and women (aged 60 to 80 years) who had high risk for cardiovascular disease. Participants were assigned to a control group or to one of two Mediterranean diets. The control group received education on following a low-fat diet, while the groups on Mediterranean diets received nutritional education and also free foods; either extra virgin olive oil, or nuts. Trained personnel measured participants’ BP at baseline and once yearly during a 4-year follow-up. We used generalized estimating equations to assess the differences between groups during the follow-up.ResultsThe percentage of participants with controlled BP increased in all three intervention groups (P-value for within-group changes: P<0.001). Participants allocated to either of the two Mediterranean diet groups had significantly lower diastolic BP than the participants in the control group (−1.53 mmHg (95% confidence interval (CI) −2.01 to −1.04) for the Mediterranean diet supplemented with extra virgin olive oil, and −0.65 mmHg (95% CI -1.15 to −0.15) mmHg for the Mediterranean diet supplemented with nuts). No between-group differences in changes of systolic BP were seen.ConclusionsBoth the traditional Mediterranean diet and a low-fat diet exerted beneficial effects on BP and could be part of advice to patients for controlling BP. However, we found lower values of diastolic BP in the two groups promoting the Mediterranean diet with extra virgin olive oil or with nuts than in the control group.Trial registrationCurrent Controlled Trials ISRCTN3573963

Regulatory sites for splicing in human basal ganglia are enriched for disease-relevant information

Genome-wide association studies have generated an increasing number of common genetic variants associated with neurological and psychiatric disease risk. An improved understanding of the genetic control of gene expression in human brain is vital considering this is the likely modus operandum for many causal variants. However, human brain sampling complexities limit the explanatory power of brain-related expression quantitative trait loci (eQTL) and allele-specific expression (ASE) signals. We address this, using paired genomic and transcriptomic data from putamen and substantia nigra from 117 human brains, interrogating regulation at different RNA processing stages and uncovering novel transcripts. We identify disease-relevant regulatory loci, find that splicing eQTLs are enriched for regulatory information of neuron-specific genes, that ASEs provide cell-specific regulatory information with evidence for cellular specificity, and that incomplete annotation of the brain transcriptome limits interpretation of risk loci for neuropsychiatric disease. This resource of regulatory data is accessible through our web server, http://braineacv2.inf.um.es/

Identification of novel risk loci, causal insights, and heritable risk for Parkinson's disease: a meta-analysis of genome-wide association studies

Background Genome-wide association studies (GWAS) in Parkinson's disease have increased the scope of biological knowledge about the disease over the past decade. We aimed to use the largest aggregate of GWAS data to identify novel risk loci and gain further insight into the causes of Parkinson's disease. Methods We did a meta-analysis of 17 datasets from Parkinson's disease GWAS available from European ancestry samples to nominate novel loci for disease risk. These datasets incorporated all available data. We then used these data to estimate heritable risk and develop predictive models of this heritability. We also used large gene expression and methylation resources to examine possible functional consequences as well as tissue, cell type, and biological pathway enrichments for the identified risk factors. Additionally, we examined shared genetic risk between Parkinson's disease and other phenotypes of interest via genetic correlations followed by Mendelian randomisation. Findings Between Oct 1, 2017, and Aug 9, 2018, we analysed 7·8 million single nucleotide polymorphisms in 37 688 cases, 18 618 UK Biobank proxy-cases (ie, individuals who do not have Parkinson's disease but have a first degree relative that does), and 1·4 million controls. We identified 90 independent genome-wide significant risk signals across 78 genomic regions, including 38 novel independent risk signals in 37 loci. These 90 variants explained 16–36% of the heritable risk of Parkinson's disease depending on prevalence. Integrating methylation and expression data within a Mendelian randomisation framework identified putatively associated genes at 70 risk signals underlying GWAS loci for follow-up functional studies. Tissue-specific expression enrichment analyses suggested Parkinson's disease loci were heavily brain-enriched, with specific neuronal cell types being implicated from single cell data. We found significant genetic correlations with brain volumes (false discovery rate-adjusted p=0·0035 for intracranial volume, p=0·024 for putamen volume), smoking status (p=0·024), and educational attainment (p=0·038). Mendelian randomisation between cognitive performance and Parkinson's disease risk showed a robust association (p=8·00 × 10−7). Interpretation These data provide the most comprehensive survey of genetic risk within Parkinson's disease to date, to the best of our knowledge, by revealing many additional Parkinson's disease risk loci, providing a biological context for these risk factors, and showing that a considerable genetic component of this disease remains unidentified. These associations derived from European ancestry datasets will need to be followed-up with more diverse data. Funding The National Institute on Aging at the National Institutes of Health (USA), The Michael J Fox Foundation, and The Parkinson's Foundation (see appendix for full list of funding sources)

Moving beyond neurons: the role of cell type-specific gene regulation in Parkinson's disease heritability

Parkinson’s disease (PD), with its characteristic loss of nigrostriatal dopaminergic neurons and deposition of α-synuclein in neurons, is often considered a neuronal disorder. However, in recent years substantial evidence has emerged to implicate glial cell types, such as astrocytes and microglia. In this study, we used stratified LD score regression and expression-weighted cell-type enrichment together with several brain-related and cell-type-specific genomic annotations to connect human genomic PD findings to specific brain cell types. We found that PD heritability attributable to common variation does not enrich in global and regional brain annotations or brain-related cell-type-specific annotations. Likewise, we found no enrichment of PD susceptibility genes in brain-related cell types. In contrast, we demonstrated a significant enrichment of PD heritability in a curated lysosomal gene set highly expressed in astrocytic, microglial, and oligodendrocyte subtypes, and in LoF-intolerant genes, which were found highly expressed in almost all tested cellular subtypes. Our results suggest that PD risk loci do not lie in specific cell types or individual brain regions, but rather in global cellular processes detectable across several cell types

RICORS2040 : The need for collaborative research in chronic kidney disease

Chronic kidney disease (CKD) is a silent and poorly known killer. The current concept of CKD is relatively young and uptake by the public, physicians and health authorities is not widespread. Physicians still confuse CKD with chronic kidney insufficiency or failure. For the wider public and health authorities, CKD evokes kidney replacement therapy (KRT). In Spain, the prevalence of KRT is 0.13%. Thus health authorities may consider CKD a non-issue: very few persons eventually need KRT and, for those in whom kidneys fail, the problem is 'solved' by dialysis or kidney transplantation. However, KRT is the tip of the iceberg in the burden of CKD. The main burden of CKD is accelerated ageing and premature death. The cut-off points for kidney function and kidney damage indexes that define CKD also mark an increased risk for all-cause premature death. CKD is the most prevalent risk factor for lethal coronavirus disease 2019 (COVID-19) and the factor that most increases the risk of death in COVID-19, after old age. Men and women undergoing KRT still have an annual mortality that is 10- to 100-fold higher than similar-age peers, and life expectancy is shortened by ~40 years for young persons on dialysis and by 15 years for young persons with a functioning kidney graft. CKD is expected to become the fifth greatest global cause of death by 2040 and the second greatest cause of death in Spain before the end of the century, a time when one in four Spaniards will have CKD. However, by 2022, CKD will become the only top-15 global predicted cause of death that is not supported by a dedicated well-funded Centres for Biomedical Research (CIBER) network structure in Spain. Realizing the underestimation of the CKD burden of disease by health authorities, the Decade of the Kidney initiative for 2020-2030 was launched by the American Association of Kidney Patients and the European Kidney Health Alliance. Leading Spanish kidney researchers grouped in the kidney collaborative research network Red de Investigación Renal have now applied for the Redes de Investigación Cooperativa Orientadas a Resultados en Salud (RICORS) call for collaborative research in Spain with the support of the Spanish Society of Nephrology, Federación Nacional de Asociaciones para la Lucha Contra las Enfermedades del Riñón and ONT: RICORS2040 aims to prevent the dire predictions for the global 2040 burden of CKD from becoming true