Search of symmetric composition methods of symmetric integrators

Composition methods are useful when solving Ordinary Differential Equations (ODEs) as they increase the order of accuracy of a given basic numerical integration scheme. We will focus on sy-mmetric composition methods involving some basic second order symmetric integrator with different step sizes [17]. The introduction of symmetries into these methods simplifies the order conditions and reduces the number of unknowns. Several authors have worked in the search of the coefficients of these type of methods: the best method of order 8 has 17 stages [24], methods of order 8 and 15 stages were given in [29, 39, 40], 10-order methods of 31, 33 and 35 stages have been also found [24, 34]. In this work some techniques that we have built to obtain 10-order symmetric composition methods of symmetric integrators of s = 31 stages (16 order conditions) are explored. Given some starting coefficients that satisfy the simplest five order conditions, the process followed to obtain the coefficients that satisfy the sixteen order conditions is provided.

Evaluation of Alpha 1-Antitrypsin and the Levels of mRNA Expression of Matrix Metalloproteinase 7, Urokinase Type Plasminogen Activator Receptor and COX-2 for the Diagnosis of Colorectal Cancer

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Mechanisms Responsible for the Trophic Effect of Beta-Adrenoceptors on the I-to Current Density in Type 1 Diabetic Rat Cardiomyocytes

Background/Aims: In diabetic ventricular myocytes, transient outward potassium current (I-to) amplitude is severely reduced because of the impaired catecholamine release that characterizes diabetic autonomic neuropathy. Sympathetic nervous system exhibits a trophic effect on I-to since incubation of myocytes with noradrenaline restores current amplitude via beta-adrenoceptor (beta AR) stimulation. Here, we investigate the intracellular signalling pathway though which incubation of diabetic cardiomyocytes with the beta AR agonist isoproterenol recovers I-to amplitude to normal values. Methods: Experiments were performed in ventricular myocytes isolated from streptozotocin-diabetic rats. I-to current was recorded by using the patch-clamp technique. Kv4 channel expression was determined by immunofluorescence. Protein-protein interaction was determined by coimmunoprecipitation. Results: Stimulation of beta AR activates first a G alpha s protein, adenylyl cyclase and Protein Kinase A. PKA-phosphorylated receptor then switches to the G alpha i protein. This leads to the activation of the beta AR-Kinase-1 and further receptor phosphorylation and arrestin dependent internalization. The internalized receptor-arrestin complex recruits and activates cSrc and the MAPK cascade, where Ras, c-Raf1 and finally ERK1/2 mediate the increase in Kv4.2 and Kv4.3 protein abundance in the plasma membrane. Conclusion: beta(2)AR stimulation activates a G alpha s and G alpha i protein dependent pathway where the ERK1/2 modulates the Ito current amplitude and the density of the Kv4.2 and Kv4.2 channels in the plasma membrane upon sympathetic stimulation in diabetic heart.

Expression and activity profiles of DPP IV/CD26 and NEP/CD10 glycoproteins in the human renal cancer are tumor-type dependent

Background: Cell-surface glycoproteins play critical roles in cell-to-cell recognition, signal transduction and regulation, thus being crucial in cell proliferation and cancer etiogenesis and development. DPP IV and NEP are ubiquitous glycopeptidases closely linked to tumor pathogenesis and development, and they are used as markers in some cancers. In the present study, the activity and protein and mRNA expression of these glycoproteins were analysed in a subset of clear-cell (CCRCC) and chromophobe (ChRCC) renal cell carcinomas, and in renal oncocytomas (RO). Methods: Peptidase activities were measured by conventional enzymatic assays with fluorogen-derived substrates. Gene expression was quantitatively determined by qRT-PCR and membrane-bound protein expression and distribution analysis was performed by specific immunostaining. Results: The activity of both glycoproteins was sharply decreased in the three histological types of renal tumors. Protein and mRNA expression was strongly downregulated in tumors from distal nephron (ChRCC and RO). Moreover, soluble DPP IV activity positively correlated with the aggressiveness of CCRCCs (higher activities in high grade tumors). Conclusions: These results support the pivotal role for DPP IV and NEP in the malignant transformation pathways and point to these peptidases as potential diagnostic markers.

The prevalence of diabetes-related complications and multimorbidity in the population with type 2 diabetes mellitus in the Basque Country

Background: Type 2 diabetes mellitus is associated with a diverse range of pathologies. The aim of the study was to determine the incidence of diabetes-related complications, the prevalence of coexistent chronic conditions and to report multimorbidity in people with type 2 diabetes living in the Basque Country. Methods: Administrative databases, in four cross sections (annually from 2007 to 2011) were consulted to analyse 149,015 individual records from patients aged >= 35 years with type 2 diabetes mellitus. The data observed were: age, sex, diabetes-related complications (annual rates of acute myocardial infarction, major amputations and avoidable hospitalisations), diabetes-related pathologies (prevalence of ischaemic heart disease, renal failure, stroke, heart failure, peripheral neuropathy, foot ulcers and diabetic retinopathy) and other unrelated pathologies (44 diseases). Results: The annual incidence for each condition progressively decreased during the four-year period: acute myocardial infarction (0.47 to 0.40%), major amputations (0.10 to 0.08%), and avoidable hospitalisations (5.85 to 5.5%). The prevalence for diabetes-related chronic pathologies was: ischaemic heart disease (11.5%), renal failure (8.4%), stroke (7.0%), heart failure (4.3%), peripheral neuropathy (1.3%), foot ulcers (2.0%) and diabetic retinopathy (7.2%). The prevalence of multimorbidity was 90.4%. The highest prevalence for other chronic conditions was 73.7% for hypertension, 13.8% for dyspepsia and 12.7% for anxiety. Conclusions: In the type 2 diabetes mellitus population living in the Basque Country, incidence rates of diabetes complications are not as high as in other places. However, they present a high prevalence of diabetes related and unrelated diseases. Multimorbidity is very common in this group, and is a factor to be taken into account to ensure correct clinical management.