A simple demonstration of the existence of the jordan canonical form for any square matrix

All the demonstrations known to this author of the existence of the Jordan Canonical Form aresomewhat complex - usually invoking the use of new spaces, and what not. These demonstrationsare usually too difficult for an average Mathematics student to understand how he or she can obtainthe Jordan Canonical Form for any square matrix. The method here proposed not only demonstratesthe existence of such forms but, additionally, shows how to find them in a step by step manner. I donot claim that the following demonstration is in any way “elegant” (by the standards of elegance infashion nowadays among mathematicians) but merely simple (undergraduate students taking a fistcourse in Matrix Algebra would understand how it works).

Sociedades e Mudanças Sociais

Neste Texto Tentamos Mostrar como o Processo de Desenvolvimento não Pode ser Entendido como um Mero Processo de Mudança Econômica, Valendo-Nos das Contribuições dos Sociólogos Evolucionistas, para Tal.

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to <90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], >300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of <15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P<0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P<0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

DNA sequence of human chromosome 17 and analysis of rearrangement in the human lineage

Chromosome 17 is unusual among the human chromosomes in many respects. It is the largest human autosome with orthology to only a single mouse chromosome1, mapping entirely to the distal half of mouse chromosome 11. Chromosome 17 is rich in protein-coding genes, having the second highest gene density in the genome2,3. It is also enriched in segmental duplications, ranking third in density among the autosomes4. Here we report a finished sequence for human chromosome 17, as well as a structural comparison with the finished sequence for mouse chromosome 11, the first finished mouse chromosome. Comparison of the orthologous regions reveals striking differences. In contrast to the typical pattern seen in mammalian evolution5,6, the human sequence has undergone extensive intrachromosomal rearrangement, whereas the mouse sequence has been remarkably stable. Moreover, although the human sequence has a high density of segmental duplication, the mouse sequence has a very low density. Notably, these segmental duplications correspond closely to the sites of structural rearrangement, demonstrating a link between duplication and rearrangement. Examination of the main classes of duplicated segments provides insight into the dynamics underlying expansion of chromosome-specific, low-copy repeats in the human genome

Comprehensive genomic characterization defines human glioblastoma genes and core pathways

Human cancer cells typically harbour multiple chromosomal aberrations, nucleotide substitutions and epigenetic modifications that drive malignant transformation. The Cancer Genome Atlas ( TCGA) pilot project aims to assess the value of large- scale multi- dimensional analysis of these molecular characteristics in human cancer and to provide the data rapidly to the research community. Here we report the interim integrative analysis of DNA copy number, gene expression and DNA methylation aberrations in 206 glioblastomas - the most common type of primary adult brain cancer - and nucleotide sequence aberrations in 91 of the 206 glioblastomas. This analysis provides new insights into the roles of ERBB2, NF1 and TP53, uncovers frequent mutations of the phosphatidylinositol- 3- OH kinase regulatory subunit gene PIK3R1, and provides a network view of the pathways altered in the development of glioblastoma. Furthermore, integration of mutation, DNA methylation and clinical treatment data reveals a link between MGMT promoter methylation and a hypermutator phenotype consequent to mismatch repair deficiency in treated glioblastomas, an observation with potential clinical implications. Together, these findings establish the feasibility and power of TCGA, demonstrating that it can rapidly expand knowledge of the molecular basis of cancer

Whole-genome sequencing reveals host factors underlying critical COVID-19

Altres ajuts: Department of Health and Social Care (DHSC); Illumina; LifeArc; Medical Research Council (MRC); UKRI; Sepsis Research (the Fiona Elizabeth Agnew Trust); the Intensive Care Society, Wellcome Trust Senior Research Fellowship (223164/Z/21/Z); BBSRC Institute Program Support Grant to the Roslin Institute (BBS/E/D/20002172, BBS/E/D/10002070, BBS/E/D/30002275); UKRI grants (MC_PC_20004, MC_PC_19025, MC_PC_1905, MRNO2995X/1); UK Research and Innovation (MC_PC_20029); the Wellcome PhD training fellowship for clinicians (204979/Z/16/Z); the Edinburgh Clinical Academic Track (ECAT) programme; the National Institute for Health Research, the Wellcome Trust; the MRC; Cancer Research UK; the DHSC; NHS England; the Smilow family; the National Center for Advancing Translational Sciences of the National Institutes of Health (CTSA award number UL1TR001878); the Perelman School of Medicine at the University of Pennsylvania; National Institute on Aging (NIA U01AG009740); the National Institute on Aging (RC2 AG036495, RC4 AG039029); the Common Fund of the Office of the Director of the National Institutes of Health; NCI; NHGRI; NHLBI; NIDA; NIMH; NINDS.Critical COVID-19 is caused by immune-mediated inflammatory lung injury. Host genetic variation influences the development of illness requiring critical care or hospitalization after infection with SARS-CoV-2. The GenOMICC (Genetics of Mortality in Critical Care) study enables the comparison of genomes from individuals who are critically ill with those of population controls to find underlying disease mechanisms. Here we use whole-genome sequencing in 7,491 critically ill individuals compared with 48,400 controls to discover and replicate 23 independent variants that significantly predispose to critical COVID-19. We identify 16 new independent associations, including variants within genes that are involved in interferon signalling (IL10RB and PLSCR1), leucocyte differentiation (BCL11A) and blood-type antigen secretor status (FUT2). Using transcriptome-wide association and colocalization to infer the effect of gene expression on disease severity, we find evidence that implicates multiple genes-including reduced expression of a membrane flippase (ATP11A), and increased expression of a mucin (MUC1)-in critical disease. Mendelian randomization provides evidence in support of causal roles for myeloid cell adhesion molecules (SELE, ICAM5 and CD209) and the coagulation factor F8, all of which are potentially druggable targets. Our results are broadly consistent with a multi-component model of COVID-19 pathophysiology, in which at least two distinct mechanisms can predispose to life-threatening disease: failure to control viral replication; or an enhanced tendency towards pulmonary inflammation and intravascular coagulation. We show that comparison between cases of critical illness and population controls is highly efficient for the detection of therapeutically relevant mechanisms of disease