Toeplitz matrix method and nonlinear integral equation of Hammerstein type

AbstractThe existence and uniqueness solution of the nonlinear integral equation of Hammerstein type with discontinuous kernel are discussed. The normality and continuity of the integral operator are proved. Toeplitz matrix method is used, as a numerical method, to obtain a nonlinear system of algebraic equations. Also, many important theorems related to the existence and uniqueness of the produced algebraic system are derived. Finally, numerical examples, when the kernel takes a logarithmic and Carleman forms, are discussed and the estimate error, in each case, is calculated

Noninvasive diagnosis of coronary artery stenosis in women with limited exercise capacity: comparison of dobutamine stress echocardiography and 99mTc sestamibi single-photon emission CT

OBJECTIVES: To compare the accuracy of dobutamine stress echocardiography (DSE) and simultaneous 99mTc sestamibi (MIBI) single-photon emission CT (SPECT) imaging for the diagnosis of coronary artery stenosis in women. PATIENTS: Seventy women with limited exercise capacity referred for evaluation of myocardial ischemia. METHODS: DSE (up to 40 microg/kg/min) was performed in conjunction with stress MIBI SPECT. Resting MIBI images were acquired 24 h after the stress test. Ischemia was defined as new or worsened wall motion abnormalities confirmed by DSE and as reversible perfusion defects confirmed by MIBI. Significant coronary artery disease was defined as > or = 50% luminal diameter stenosis. RESULTS: DSE was positive for ischemia in 35 of 45 patients with coronary artery stenosis and in 2 of 25 patients without coronary artery stenosis (sensitivity = 78% CI, 68 to 88; specificity = 92% CI, 85 to 99; and accuracy = 83% CI, 74 to 92). A positive MIBI study for ischemia occurred in 29 patients with coronary artery stenosis and in 7 patients without coronary artery stenosis (sensitivity = 64% CI, 53 to 76; specificity = 72% CI, 61 to 83; and accuracy = 67% CI, 56 to 78 [p < 0.05 vs DSE]). In the 59 vascular regions with coronary artery stenosis, the regional sensitivity of DSE was higher than MIBI (69% CI, 62 to 77 vs 51% CI, 42 to 59, p < 0.05), whereas specificity in the 81 vascular regions without significant stenosis was similar (89% CI, 84 to 94 vs 88% CI, 82 to 93, respectively). CONCLUSION: DSE is a useful noninvasive method for the diagnosis of coronary artery stenosis in women and provides a higher overall and regional diagnostic accuracy than dobutamine MIBI SPECT in this particular population

Assessment of patients after coronary artery bypass grafting by dobutamine stress echocardiography

Dobutamine stress echocardiography is an accurate method for the diagnosis and localization of vascular compromise in patients evaluated after coronary artery bypass graft surgery. The test provides useful data for selection of patients for whom coronary angiography may be indicated

Impact of severity of coronary artery stenosis and the collateral circulation on the functional outcome of dyssynergic myocardium after revascularization in patients with healed myocardial infarction and chronic left ventricular dysfunction

The aim of this study was to assess the influence of the severity of coronary artery stenosis and the grade of collateral circulation on myocardial viability in patients with chronic left ventricular (LV) dysfunction undergoing coronary artery bypass grafting. Forty patients (age 59 ± 8 years) with old myocardial infarction were studied by dobutamine stress echocardiogrophy (DSE) before coronary artery bypass grafting. LV function was assessed using a 16-segment, 5-grade score model. Viability and functional recovery were respectively defined as a reduction in wall motion score ≤ 1 at low-dose DSE and at follow-up echocardiograms obtained 3 months after surgery. There were 56 stenotic coronary arteries subtending severely dyssynergic myocardial segments, of which 38 were occluded. Among 186 severely dyssynergic segments, functional recovery occurred in 42 (23%). There was no significant difference between myocardial regions with patent or occluded coronary arteries with respect to prevalence of viability or functional recovery and percentage of viable or recovered segments relative to the total number of dyssynergic segments. In patients with total occlusion, these parameters were not different between regions with different collateral grades. Sensitivity, specificity, and accuracy of low-dose DSE for prediction of regional functional recovery were 71%, 90%, and 86%, r

Gender differences in the accuracy of dobutamine stress echocardiography for the diagnosis of coronary artery disease

The accuracy of dobutamine stress echocardiography (DSE) for the diagnosis of coronary artery disease (CAD) has not been yet evaluated in women. We studied the effect of gender on the accuracy of DSE for the diagnosis of CAD in 306 consecutive patients (210 men and 96 women) with limited exercise capacity and suspected myocardial ischemia who underwent coronary angiography within 3 months of DSE. There were no serious complications during DSE. Men had a higher prevalence of nonsustained ventricular tachycardia (7% vs 0.03%, p <0.05) and supraventricular tachycardia (9% vs 0.03%, p <0.05) during the test compared with women. Peak stress rate-pressure product was not different in men and women (18,140 ± 4,187 vs 18,543 ± 4,223). Significant CAD (≤50% luminal diameter stenosis) was present in 171 men (81%) and in 62 women (65%, p <0.005). The sensitivity, specificity, and accuracy of ischemic pattern at DSE for the diagnosis of significant CAD were 76% (confidence interval [CI] 67 to 84), 94% (CI 89 to 99), and 82% (C175 to 90) in women and 73% (CI 67 to 79), 77% (CI 71 to 83), and 74% (Cl 68 to 80) in men, respectively. Overall specificity was higher in women than in men (p <0.05). Regional accuracy of DSE was significantly higher in women than in men in the 3 arterial regions (84% [CI 79 to 88] vs 75% [CI 72 to 79], p <0.005). It is concluded that DSE is a safe and feasible method for the diagnosis of CAD in women.

Detecting a stochastic gravitational wave background with the Laser Interferometer Space Antenna

The random superposition of many weak sources will produce a stochastic background of gravitational waves that may dominate the response of the LISA (Laser Interferometer Space Antenna) gravitational wave observatory. Unless something can be done to distinguish between a stochastic background and detector noise, the two will combine to form an effective noise floor for the detector. Two methods have been proposed to solve this problem. The first is to cross-correlate the output of two independent interferometers. The second is an ingenious scheme for monitoring the instrument noise by operating LISA as a Sagnac interferometer. Here we derive the optimal orbital alignment for cross-correlating a pair of LISA detectors, and provide the first analytic derivation of the Sagnac sensitivity curve.Comment: 9 pages, 11 figures. Significant changes to the noise estimate

Relation between ST segment elevation during dobutamine stress test and myocardial viability after a recent m

OBJECTIVE: To assess the relation between ST segment elevation during the dobutamine stress test and late improvement of function after acute Q wave myocardial infarction. PATIENTS AND DESIGN: 70 patients were studied a mean (SD) 8 (3) days after acute myocardial infarction with high dose dobutamine-atropine stress echocardiography and a follow up echocardiogram at 85 (10) days. A score model based on 16 segments and four grades was used to assess left ventricular function. Functional improvement was defined as a reduction of wall motion score > or = 1 in > or = 1 segments at follow up. INTERVENTION: Myocardial revascularisation was performed in 23 patients (33%) before follow up studies. RESULTS: ST segment elevation occurred in 40 patients (57%). Late functional improvement occurred in 35 patients (50%). Functional improvement was more common in patients with ST segment elevation (68% v 30%, P < 0.005) and they had a higher mean (SD) number of improved segments at follow up (1.9 (2.2) v 0.5 (1.1), P < 0.005). The wall motion score index decreased between baseline and follow up in patients with ST segment elevation (1.54 (0.50) v 1.48 (0.43), P < 0.05) but not in patients without ST segment elevation (1.39 (0.60) v 1.45 (0.47)). The accuracy of ST segment elevation for the prediction of functional improvement was similar to that of low dose dobutamine echocardiography in patients with anterior infarction (80% v 83%) and in patients who underwent revascularisation (78% v 83% respectively). CONCLUSION: In patients with a recent Q wave myocardial infarction, dobutamine-induced ST segment elevation is a valuable marker of myocardial viability particularly when the test is performed without or with suboptimal echocardiographic imaging

The Polygenic and Monogenic Basis of Blood Traits and Diseases

Blood cells play essential roles in human health, underpinning physiological processes such as immunity, oxygen transport, and clotting, which when perturbed cause a significant global health burden. Here we integrate data from UK Biobank and a large-scale international collaborative effort, including data for 563,085 European ancestry participants, and discover 5,106 new genetic variants independently associated with 29 blood cell phenotypes covering a range of variation impacting hematopoiesis. We holistically characterize the genetic architecture of hematopoiesis, assess the relevance of the omnigenic model to blood cell phenotypes, delineate relevant hematopoietic cell states influenced by regulatory genetic variants and gene networks, identify novel splice-altering variants mediating the associations, and assess the polygenic prediction potential for blood traits and clinical disorders at the interface of complex and Mendelian genetics. These results show the power of large-scale blood cell trait GWAS to interrogate clinically meaningful variants across a wide allelic spectrum of human variation. Analysis of blood cell traits in the UK Biobank and other cohorts illuminates the full genetic architecture of hematopoietic phenotypes, with evidence supporting the omnigenic model for complex traits and linking polygenic burden with monogenic blood diseases

The Polygenic and Monogenic Basis of Blood Traits and Diseases

Blood cells play essential roles in human health, underpinning physiological processes such as immunity, oxygen transport, and clotting, which when perturbed cause a significant global health burden. Here we integrate data from UK Biobank and a large-scale international collaborative effort, including data for 563,085 European ancestry participants, and discover 5,106 new genetic variants independently associated with 29 blood cell phenotypes covering a range of variation impacting hematopoiesis. We holistically characterize the genetic architecture of hematopoiesis, assess the relevance of the omnigenic model to blood cell phenotypes, delineate relevant hematopoietic cell states influenced by regulatory genetic variants and gene networks, identify novel splice-altering variants mediating the associations, and assess the polygenic prediction potential for blood traits and clinical disorders at the interface of complex and Mendelian genetics. These results show the power of large-scale blood cell trait GWAS to interrogate clinically meaningful variants across a wide allelic spectrum of human variation.</p

Trans-ethnic and Ancestry-Specific Blood-Cell Genetics in 746,667 Individuals from 5 Global Populations

Most loci identified by GWASs have been found in populations of European ancestry (EUR). In trans-ethnic meta-analyses for 15 hematological traits in 746,667 participants, including 184,535 non-EUR individuals, we identified 5,552 trait-variant associations at p &lt; 5 × 10−9, including 71 novel associations not found in EUR populations. We also identified 28 additional novel variants in ancestry-specific, non-EUR meta-analyses, including an IL7 missense variant in South Asians associated with lymphocyte count in vivo and IL-7 secretion levels in vitro. Fine-mapping prioritized variants annotated as functional and generated 95% credible sets that were 30% smaller when using the trans-ethnic as opposed to the EUR-only results. We explored the clinical significance and predictive value of trans-ethnic variants in multiple populations and compared genetic architecture and the effect of natural selection on these blood phenotypes between populations. Altogether, our results for hematological traits highlight the value of a more global representation of populations in genetic studies. Delineation of the genetic architecture of hematological traits in a multi-ethnic dataset allows identification of rare variants with strong effects specific to non-European populations and improved fine mapping of GWAS variants using the trans-ethnic approach