The nonexistence of spurious solutions to discrete, two-point boundary value problems

We investigate difference equations which arise as discrete approximations to two-point boundary value problems for systems of second-order, ordinary differential equations. We formulate conditions under which all solutions to the discrete problem satisfy certain a priori bounds which axe independent of the step-size. As a result, the nonexistence of spurious solutions are guaranteed. Some existence and convergence theorems for solutions to the discrete problem are also presented. (C) 2002 Elsevier Science Ltd. All rights reserved.

Morphology, ultrastructure, and implied function of ciliated sensory structures on the developmental stages of Merizocotyle icopae (Monogenea : Monocotylidae)

Experimental infections were used to track the fate of the dorsal sensilla of Merizocotyle icopae (Monogenea: Monocotylidae) from nasal tissue of the shovelnose ray, Rhinobatos typus (Rhinobatidae). Scanning and transmission electron microscopy revealed that 3 types of uniciliate dorsal sensilla exist at different times in the development of the monogenean. Type 1 sensilla have little or no invagination where the cilium exits the distal end of the dendrite and possess a ring of epidermis surrounding the cilium distal to the invagination. Type 2 sensilla have a deep invagination where the cilium exits the dendrite. Type 3 sensilla can be distinguished from the other types by the shape of the dendrite. The larvae have predominantly Type I dorsal sensilla, most of which are lost approximately 24 h after infection and a few Type 2 sensilla, which are retained. Additional Type 2 sensilla (termed Adult Type 2 sensilla), which are slightly different morphologically from the Type 2 sensilla of the larvae, form in later stages of development. Numerous Type 3 sensilla are unique to the dorsal surface of adults. Loss of all Type I sensilla upon attachment to the host, R. typus, suggests that these may be chemo- or mechanoreceptors responsible for host location by the swimming infective larvae. Type 2 sensilla appear to be important in the larvae, juveniles, and adults whereas the modality mediated by Type 3 is specific to adults. (C) 2003 Wiley-Liss, Inc.

Identification of residues and domains of Raf important for function in vivo and in vitro

Random mutagenesis and genetic screens for impaired Raf function in Caenorhabditis elegans were used to identify six loss-of-function alleles of lin-45 raf that result in a substitution of a single amino acid. The mutations were classified as weak, intermediate, and strong based on phenotypic severity. We engineered these mutations into the homologous residues of vertebrate Raf-1 and analyzed the mutant proteins for their underlying biochemical defects. Surprisingly, phenotype strength did not correlate with the catalytic activity of the mutant proteins. Amino acid substitutions Val-589 and Ser-619 severely compromised Raf kinase activity, yet these mutants displayed weak phenotypes in the genetic screen. Interestingly, this is because these mutant Raf proteins efficiently activate the MAPK (mitogen-activated protein kinase) cascade in living cells, a result that may inform the analysis of knockout mice. Equally intriguing was the observation that mutant proteins with non-functional Ras-binding domains, and thereby deficient in Ras-mediated membrane recruitment, displayed only intermediate strength phenotypes. This confirms that secondary mechanisms exist to couple Ras to Raf in vivo. The strongest phenotype in the genetic screens was displayed by a S508N mutation that again did not correlate with a significant loss of kinase activity or membrane recruitment by oncogenic Ras in biochemical assays. Ser-508 lies within the Raf-1 activation loop, and mutation of this residue in Raf-1 and the equivalent Ser-615 in B-Raf revealed that this residue regulates Raf binding to MEK. Further characterization revealed that in response to activation by epidermal growth factor, the Raf-S508N mutant protein displayed both reduced catalytic activity and aberrant activation kinetics: characteristics that may explain the C. elegans phenotype.

Impulse-response function of splanchnic circulation with model-independent constraints: theory and experimental validation

Modeling physiological processes using tracer kinetic methods requires knowledge of the time course of the tracer concentration in blood supplying the organ. For liver studies, however, inaccessibility of the portal vein makes direct measurement of the hepatic dual-input function impossible in humans. We want to develop a method to predict the portal venous time-activity curve from measurements of an arterial time-activity curve. An impulse-response function based on a continuous distribution of washout constants is developed and validated for the gut. Experiments with simultaneous blood sampling in aorta and portal vein were made in 13 anesthetized pigs following inhalation of intravascular [O-15] CO or injections of diffusible 3-O[ C-11] methylglucose (MG). The parameters of the impulse-response function have a physiological interpretation in terms of the distribution of washout constants and are mathematically equivalent to the mean transit time ( T) and standard deviation of transit times. The results include estimates of mean transit times from the aorta to the portal vein in pigs: (T) over bar = 0.35 +/- 0.05 min for CO and 1.7 +/- 0.1 min for MG. The prediction of the portal venous time-activity curve benefits from constraining the regression fits by parameters estimated independently. This is strong evidence for the physiological relevance of the impulse-response function, which includes asymptotically, and thereby justifies kinetically, a useful and simple power law. Similarity between our parameter estimates in pigs and parameter estimates in normal humans suggests that the proposed model can be adapted for use in humans.

Existence of multiple solutions for finite difference approximations to second-order boundary value problems

Error condition detected We consider discrete two-point boundary value problems of the form D-2 y(k+1) = f (kh, y(k), D y(k)), for k = 1,...,n - 1, (0,0) = G((y(0),y(n));(Dy-1,Dy-n)), where Dy-k = (y(k) - Yk-I)/h and h = 1/n. This arises as a finite difference approximation to y" = f(x,y,y'), x is an element of [0,1], (0,0) = G((y(0),y(1));(y'(0),y'(1))). We assume that f and G = (g(0), g(1)) are continuous and fully nonlinear, that there exist pairs of strict lower and strict upper solutions for the continuous problem, and that f and G satisfy additional assumptions that are known to yield a priori bounds on, and to guarantee the existence of solutions of the continuous problem. Under these assumptions we show that there are at least three distinct solutions of the discrete approximation which approximate solutions to the continuous problem as the grid size, h, goes to 0. (C) 2003 Elsevier Science Ltd. All rights reserved.

An augmented Lanczos algorithm for the efficient computation of a dot-product of a function of a large sparse symmetric matrix

The Lanczos algorithm is appreciated in many situations due to its speed. and economy of storage. However, the advantage that the Lanczos basis vectors need not be kept is lost when the algorithm is used to compute the action of a matrix function on a vector. Either the basis vectors need to be kept, or the Lanczos process needs to be applied twice. In this study we describe an augmented Lanczos algorithm to compute a dot product relative to a function of a large sparse symmetric matrix, without keeping the basis vectors.

The value of screening in siblings of patients with abdominal aortic aneurysm

Objectives. This study aimed to determine the incidence of abdominal aortic aneurysm (AAA) in a large group of siblings of Australian AAA patients to determine if screening in this group is justified. Methods. 1254 siblings of 400 index AAA patients were identified and offered aortic ultrasound screening. An age and sex matched control group was recruited from patients having abdominal CT scans for non-vascular indications. AAA was defined by an infrarenal aortic diameter of greater than or equal to3 cm or a ratio of the infrarenal to suprarenal aortic diameter of greater than or equal to2.0. A ratio of 1.0-1.5 was considered normal, and a ratio of >1.5 to

A modified Weibull distribution

A new lifetime distribution capable of modeling a bathtub-shaped hazard-rate function is proposed. The proposed model is derived as a limiting case of the Beta Integrated Model and has both the Weibull distribution and Type I extreme value distribution as special cases. The model can be considered as another useful 3-parameter generalization of the Weibull distribution. An advantage of the model is that the model parameters can be estimated easily based on a Weibull probability paper (WPP) plot that serves as a tool for model identification. Model characterization based on the WPP plot is studied. A numerical example is provided and comparison with another Weibull extension, the exponentiated Weibull, is also discussed. The proposed model compares well with other competing models to fit data that exhibits a bathtub-shaped hazard-rate function.

Analysis of the mouse transcriptome for genes involved in the function of the nervous system

We analyzed the mouse Representative Transcript and Protein Set for molecules involved in brain function. We found full-length cDNAs of many known brain genes and discovered new members of known brain gene families, including Family 3 G-protein coupled receptors, voltage-gated channels, and connexins. We also identified previously unknown candidates for secreted neuroactive molecules. The existence of a large number of unique brain ESTs suggests an additional molecular complexity that remains to be explored. A list of genes containing CAG stretches in the coding region represents a first step in the potential identification of candidates for hereditary neurological disorders.

The value of idiosyncratic markers and changes to conserved tRNA sequences from the mitochondrial genome of hard ticks (Acari: Ixodida: Ixodidae) for phylogenetic inference

Idiosyncratic markers are features of genes and genomes that are so unusual that it is unlikely that they evolved more than once in a lineage of organisms. Here we explore further the potential of idiosyncratic markers and changes to typically conserved tRNA sequences for phylogenetic inference. Hard ticks were chosen as the model group because their phylogeny has been studied extensively. Fifty-eight candidate markers from hard ticks ( family Ixodidae) and 22 markers from the subfamily Rhipicephalinae sensu lato were mapped onto phylogenies of these groups. Two of the most interesting markers, features of the secondary structure of two different tRNAs, gave strong support to the hypothesis that species of the Prostriata ( Ixodes spp.) are monophyletic. Previous analyses of genes and morphology did not strongly support this relationship, instead suggesting that the Prostriata is paraphyletic with respect to the Metastriata ( the rest of the hard ticks). Parallel or convergent evolution was not found in the arrangements of mitochondrial genes in ticks nor were there any reversals to the ancestral arthropod character state. Many of the markers identified were phylogenetically informative, whereas others should be informative with study of additional taxa. Idiosyncratic markers and changes to typically conserved nucleotides in tRNAs that are phylogenetically informative were common in this data set, and thus these types of markers might be found in other organisms.

Alterations in pulmonary vascular function in rats exposed to intermittent hypoxia

Vasoactive agents were examined in arteries from control rats and rats exposed to intermittent hypoxia (10% oxygen; 8 h/day) for 3, 5 or 20 days. Hypoxic rats developed right ventricular hypertrophy after 5 days, but became pulmonary hypertensive (elevated right ventricular systolic pressure; RVSP) only after 20 days. In pulmonary arteries (main and intralobar), responses to acetylcholine and ionomycin (endothelium-dependent vasodilators) were reduced after 20 and 5 days of intermittent hypoxia, whereas contractions to 5-hydroxytryptamine (5-HT) were enhanced (potency increase >10-fold) after 20, 5 and 3 days. Contractions to endothelin-1 and a thromboxane-mimetic, but not Ca-2divided by, were also increased. No changes in vascular function occurred in aorta. Since changes in pulmonary vascular function preceded the increase in RVSP they do not result from, but may contribute to, the development of hypoxia-induced pulmonary hypertension. If similar changes occur in humans, they may be important in conditions characterised by intermittent, as opposed to continuous, hypoxia. (C) 2003 Elsevier B.V. All rights reserved.

A randomized trial of aggressive lipid reduction for improvement of myocardial ischemia, symptom status, and vascular function in patients with coronary artery disease not amenable to intervention

PURPOSE: To determine the effects of aggressive lipid lowering on markers of ischemia, resistance vessel function, atherosclerotic burden, and Symptom status in patients with symptomatic coronary artery disease. METHODS: Sixty consecutive patients with coronary artery disease that was unsuitable for revascularization were assigned randomly to either usual therapy of lipids for patients with a low-density lipoprotein (LDL) cholesterol target level <116 mg/dL, or to a, more aggressive lipid-lowering strategy involving up to 80 mg/d of atorvastatin, with a target LDL cholesterol level <77 mg/dL. The extent and severity of inducible ischemia (by dobutamine echocardiography), vascular function.(brachial artery reactivity), atheroma burden (carotid intima-media thickness), and symptom status were evaluated blindly at baseline and after 12 weeks of treatment. RESULTS: After 12 weeks of treatment, patients in the aggressive therapy group had a significantly greater decrease in mean (+/- SD) LDL cholesterol level than those in the usual care group (29 +/- 38 mg/dL vs. 7 +/- 24 mg/dL, P = 0.03). Patients in the aggressive therapy group had a reduction in the number of ischemic wall segments (mean between-group difference of 1.3; 95% confidence interval: 0.1 to 2.0; P = 0.04), flow-mediated dilatation (mean between-group difference of 5.9%; 95% confidence interval: 2.5% to 9.4%; P = 0.001), and angina score after 12 weeks. There were no significant changes in atherosclerotic burden in either group. CONCLUSION: Patients with symptomatic coronary artery disease who are treated with aggressive lipid lowering have improvement of symptom status and ischemia that appears to reflect improved vascular function but not atheroma burden. Am J Med. 2003;114:445-453. (C) 2003 by Excerpta Medica Inc.