The interval inclusion number of a partially ordered set

AbstractA containment representation for a poset P is a map ƒ such that x<y in P if and only if ƒ(x) ⊂ ƒ(y). We introduce the interval inclusion number (or interval number) i(P) as the smallest t such that P has a containment representation f in which each f(x) is the union of at most t intervals. Trivially, i(P)=1 if and only if dim(P)⩽2. Posets with i(P)=2 include the standard n-dimensional poset and all interval orders; i.e. posets of arbitrarily high dimension. In general we have the upper bound i(P) ⩽ ⌈;dim(P)2⌉, with equality holding for the Boolean algebras. For lexicographic composition, i(P) = k and dim(Q) = 2k + 1 imply i(P[Q]) = k + 1. This result and i(B2k) = k imply that testing i(P) ⩽ k for any fixed k ⩾ 2 is NP-complete. Concerning removal theorems, we prove that i(P − x) ⩾ i(P) − 1 when x is a maximal or minimal element of P, and in general i(P − x) ⩾ i(P)2

Improving protein structure similarity searches using domain boundaries based on conserved sequence information

<p>Abstract</p> <p>Background</p> <p>The identification of protein domains plays an important role in protein structure comparison. Domain query size and composition are critical to structure similarity search algorithms such as the Vector Alignment Search Tool (VAST), the method employed for computing related protein structures in NCBI Entrez system. Currently, domains identified on the basis of structural compactness are used for VAST computations. In this study, we have investigated how alternative definitions of domains derived from conserved sequence alignments in the Conserved Domain Database (CDD) would affect the domain comparisons and structure similarity search performance of VAST.</p> <p>Results</p> <p>Alternative domains, which have significantly different secondary structure composition from those based on structurally compact units, were identified based on the alignment footprints of curated protein sequence domain families. Our analysis indicates that domain boundaries disagree on roughly 8% of protein chains in the medium redundancy subset of the Molecular Modeling Database (MMDB). These conflicting sequence based domain boundaries perform slightly better than structure domains in structure similarity searches, and there are interesting cases when structure similarity search performance is markedly improved.</p> <p>Conclusion</p> <p>Structure similarity searches using domain boundaries based on conserved sequence information can provide an additional method for investigators to identify interesting similarities between proteins with known structures. Because of the improvement in performance of structure similarity searches using sequence domain boundaries, we are in the process of implementing their inclusion into the VAST search and MMDB resources in the NCBI Entrez system.</p

Database resources of the National Center for Biotechnology Information

In addition to maintaining the GenBank® nucleic acid sequence database, the National Center for Biotechnology Information (NCBI) provides analysis and retrieval resources for the data in GenBank and other biological data made available through the NCBI web site. NCBI resources include Entrez, the Entrez Programming Utilities, MyNCBI, PubMed, PubMed Central, Entrez Gene, the NCBI Taxonomy Browser, BLAST, BLAST Link (BLink), Electronic PCR, OrfFinder, Spidey, Splign, Reference Sequence, UniGene, HomoloGene, ProtEST, dbMHC, dbSNP, Cancer Chromosomes, Entrez Genomes and related tools, the Map Viewer, Model Maker, Evidence Viewer, Trace Archive, Sequence Read Archive, Retroviral Genotyping Tools, HIV-1/Human Protein Interaction Database, Gene Expression Omnibus, Entrez Probe, GENSAT, Online Mendelian Inheritance in Man, Online Mendelian Inheritance in Animals, the Molecular Modeling Database, the Conserved Domain Database, the Conserved Domain Architecture Retrieval Tool, Biosystems, Peptidome, Protein Clusters and the PubChem suite of small molecule databases. Augmenting many of the web applications are custom implementations of the BLAST program optimized to search specialized data sets. All these resources can be accessed through the NCBI home page at www.ncbi.nlm.nih.gov

Racial differences in systemic sclerosis disease presentation: a European Scleroderma Trials and Research group study

Objectives. Racial factors play a significant role in SSc. We evaluated differences in SSc presentations between white patients (WP), Asian patients (AP) and black patients (BP) and analysed the effects of geographical locations.Methods. SSc characteristics of patients from the EUSTAR cohort were cross-sectionally compared across racial groups using survival and multiple logistic regression analyses.Results. The study included 9162 WP, 341 AP and 181 BP. AP developed the first non-RP feature faster than WP but slower than BP. AP were less frequently anti-centromere (ACA; odds ratio (OR) = 0.4, P &lt; 0.001) and more frequently anti-topoisomerase-I autoantibodies (ATA) positive (OR = 1.2, P = 0.068), while BP were less likely to be ACA and ATA positive than were WP [OR(ACA) = 0.3, P &lt; 0.001; OR(ATA) = 0.5, P = 0.020]. AP had less often (OR = 0.7, P = 0.06) and BP more often (OR = 2.7, P &lt; 0.001) diffuse skin involvement than had WP.AP and BP were more likely to have pulmonary hypertension [OR(AP) = 2.6, P &lt; 0.001; OR(BP) = 2.7, P = 0.03 vs WP] and a reduced forced vital capacity [OR(AP) = 2.5, P &lt; 0.001; OR(BP) = 2.4, P &lt; 0.004] than were WP. AP more often had an impaired diffusing capacity of the lung than had BP and WP [OR(AP vs BP) = 1.9, P = 0.038; OR(AP vs WP) = 2.4, P &lt; 0.001]. After RP onset, AP and BP had a higher hazard to die than had WP [hazard ratio (HR) (AP) = 1.6, P = 0.011; HR(BP) = 2.1, P &lt; 0.001].Conclusion. Compared with WP, and mostly independent of geographical location, AP have a faster and earlier disease onset with high prevalences of ATA, pulmonary hypertension and forced vital capacity impairment and higher mortality. BP had the fastest disease onset, a high prevalence of diffuse skin involvement and nominally the highest mortality

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 &lt;90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], &gt;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 &lt;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&lt;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&lt;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

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 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 m 2), 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

Defining dry/wet spells for point observations, observed area averages, and regional climate model gridboxes in Europe

A new method for optimising threshold values of dry/wet spells is evaluated. A set of indices is used to find the best threshold giving good correspondence between the frequency of dry/wet spells in Hadley Centre regional model (HadRM3) output, reference observations with predetermined thresholds, and area-averaged observations. The analyses focus on selected model gridboxes in 3 different European climate regimes (Sweden, UK, Italy), where station data are available from several locations. In addition, a pan-European analysis using the European Climate Assessment (ECA) dataset is carried out. Generally, there is good agreement between point observations and the corresponding area average using the common thresholds of 0.1 or 1.0 mm with observational data. Applying the optimal thresholds on the model output is important, as it typically results in substantially better agreement between the simulated and observed series of dry/wet days. The fitted optimal pan-European dry/wet threshold is (1) 0.47 or 0.15 mm, depending on model version, for the observed point data threshold of 0.1 mm, and (2) 1.2 or 0.56 mm, depending on model version, for the threshold of 1.0 mm