Visualizing Rank Deficient Models: A Row Equation Geometry of Rank Deficient Matrices and Constrained-Regression

Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency. The emphasis is on the row geometry of the solutions based on the normal equations. The author shows geometrically how constrained-regression/generalized-inverses work in this situation to provide a solution in the face of rank deficiency

Selective laser trabeculoplasty: past, present, and future

Over the past two decades, selective laser trabeculoplasty (SLT) has increasingly become an established laser treatment used to lower intraocular pressure in open-angle glaucoma and ocular hypertensive patients. In this review we trace the origins of SLT from previous argon laser trabeculoplasty and review the current role it has in clinical practice. We outline future directions of SLT research and introduce emerging technologies that are further developing this intervention in the treatment paradigm of glaucoma.Eye advance online publication, 5 January 2018; doi:10.1038/eye.2017.273

Genome-wide meta-analysis reveals shared new loci in systemic seropositive rheumatic diseases

OBJECTIVE: Immune-mediated inflammatory diseases (IMIDs) are heterogeneous and complex conditions with overlapping clinical symptoms and elevated familial aggregation, which suggests the existence of a shared genetic component. In order to identify this genetic background in a systematic fashion, we performed the first cross-disease genome-wide meta-analysis in systemic seropositive rheumatic diseases, namely, systemic sclerosis, systemic lupus erythematosus, rheumatoid arthritis and idiopathic inflammatory myopathies. METHODS: We meta-analysed ~6.5 million single nucleotide polymorphisms in 11 678 cases and 19 704 non-affected controls of European descent populations. The functional roles of the associated variants were interrogated using publicly available databases. RESULTS: Our analysis revealed five shared genome-wide significant independent loci that had not been previously associated with these diseases: NAB1, KPNA4-ARL14, DGQK, LIMK1 and PRR12. All of these loci are related with immune processes such as interferon and epidermal growth factor signalling, response to methotrexate, cytoskeleton dynamics and coagulation cascade. Remarkably, several of the associated loci are known key players in autoimmunity, which supports the validity of our results. All the associated variants showed significant functional enrichment in DNase hypersensitivity sites, chromatin states and histone marks in relevant immune cells, including shared expression quantitative trait loci. Additionally, our results were significantly enriched in drugs that are being tested for the treatment of the diseases under study. CONCLUSIONS: We have identified shared new risk loci with functional value across diseases and pinpoint new potential candidate loci that could be further investigated. Our results highlight the potential of drug repositioning among related systemic seropositive rheumatic IMIDs

Identification of Novel Genetic Markers Associated with Clinical Phenotypes of Systemic Sclerosis through a Genome-Wide Association Strategy

Contains fulltext : 97006.pdf (publisher's version ) (Open Access)The aim of this study was to determine, through a genome-wide association study (GWAS), the genetic components contributing to different clinical sub-phenotypes of systemic sclerosis (SSc). We considered limited (lcSSc) and diffuse (dcSSc) cutaneous involvement, and the relationships with presence of the SSc-specific auto-antibodies, anti-centromere (ACA), and anti-topoisomerase I (ATA). Four GWAS cohorts, comprising 2,296 SSc patients and 5,171 healthy controls, were meta-analyzed looking for associations in the selected subgroups. Eighteen polymorphisms were further tested in nine independent cohorts comprising an additional 3,175 SSc patients and 4,971 controls. Conditional analysis for associated SNPs in the HLA region was performed to explore their independent association in antibody subgroups. Overall analysis showed that non-HLA polymorphism rs11642873 in IRF8 gene to be associated at GWAS level with lcSSc (P = 2.32x10(-12), OR = 0.75). Also, rs12540874 in GRB10 gene (P = 1.27 x 10(-6), OR = 1.15) and rs11047102 in SOX5 gene (P = 1.39x10(-7), OR = 1.36) showed a suggestive association with lcSSc and ACA subgroups respectively. In the HLA region, we observed highly associated allelic combinations in the HLA-DQB1 locus with ACA (P = 1.79x10(-61), OR = 2.48), in the HLA-DPA1/B1 loci with ATA (P = 4.57x10(-76), OR = 8.84), and in NOTCH4 with ACA P = 8.84x10(-21), OR = 0.55) and ATA (P = 1.14x10(-8), OR = 0.54). We have identified three new non-HLA genes (IRF8, GRB10, and SOX5) associated with SSc clinical and auto-antibody subgroups. Within the HLA region, HLA-DQB1, HLA-DPA1/B1, and NOTCH4 associations with SSc are likely confined to specific auto-antibodies. These data emphasize the differential genetic components of subphenotypes of SSc

Managing Carbon

Storing carbon (C) and offsetting carbon dioxide (CO2) emissions with the use of wood for energy, both of which slow emissions of CO2 into the atmosphere, present significant challenges for forest management (IPCC 2001). In the United States, there has been a net increase in C in forests and in harvested wood products stocks (Tables 7.1 and 7.2), a result of historical and recent ecological conditions, management practices, and use of forest products (Birdsey et al. 2006). However, recent projections for the forest sector suggest that annual C storage could begin to decline, and U.S. forests could become a net C emitter of tens to hundreds of Tg C year ¹ within a few decades (USDA FS 2012a). It is therefore urgent to identify effective C management strategies, given the complexity of factors that drive the forest C cycle and the multiple objectives for which forests are managed. An ideal C management activity contributes benefits beyond increasing C storage by achieving other management objectives and providing ecosystem services in a sustainable manner. Strategies for effectively managing forest C stocks and offsetting C emissions requires a thorough understanding of biophysical and social influences on the forest C cycle (Birdsey et al. 1993). Successful policies and incentives may be chosen to support strategies if sufficient knowledge of social processes (e.g., landowner or wood-user response to incentives and markets) is available. For example, if C stocks are expected to decrease owing to decreasing forest land area caused by exurban development, policies or incentives to avoid deforestation in those areas may be effective. If C stocks are expected to decrease owing to the effects of a warmer climate, reducing stand densities may retain C over the long term by increasing resilience to drought and other stressors and by reducing crown fire hazard (Jackson et al. 2005; Reinhardt et al. 2008). Protecting old forests and other forests that have high C stocks may be more effective than seeking C offsets associated with wood use, especially if those forests would recover C more slowly in an altered climate. If climate change increases productivity in a given area over a long period of time, increasing forest C stocks through intensive management and forest products, including biomass energy, may be especially effective. It is equally important to know which strategies might make some management practices unacceptable (e.g., reducing biodiversity). However, no standard evaluation framework exists to aid decision making on alternative management strategies for maximizing C storage while minimizing risks and tradeoffs. Here we discuss (1) where forest C is stored in the United States, (2) how to measure forest C through space and time, (3) effectiveness of various management strategies in reducing atmospheric greenhouse gases (GHG), and (4) effectiveness of incentives, regulations, and institutional arrangements for implementing C management. Understanding of biophysical and social influences on the forest C cycle (Birdsey et al. 1993). Successful policies and incentives may be chosen to support strategies if sufficient knowledge of social processes (e.g., landowner or wood-user response to incentives and markets) is available. For example, if C stocks are expected to decrease owing to decreasing forest land area caused by exurban development, policies or incentives to avoid deforestation in those areas may be effective. If C stocks are expected to decrease owing to the effects of a warmer climate, reducing stand densities may retain C over the long term by increasing resilience to drought and other stressors and by reducing crown fire hazard (Jackson et al. 2005; Reinhardt et al. 2008). Protecting old forests and other forests that have high C stocks may be more effective than seeking C offsets associated with wood use, especially if those forests would recover C more slowly in an altered climate. If climate change increases productivity in a given area over a long period of time, increasing forest C stocks through intensive management and forest products, including biomass energy, may be especially effective. It is equally important to know which strategies might make some management practices unacceptable (e.g., reducing biodiversity). However, no standard evaluation framework exists to aid decision making on alternative management strategies for maximizing C storage while minimizing risks and tradeoffs. Here we discuss (1) where forest C is stored in the United States, (2) how to measure forest C through space and time, (3) effectiveness of various management strategies in reducing atmospheric greenhouse gases (GHG), and (4) effectiveness of incentives, regulations, and institutional arrangements for implementing C management