The numerical solution of stiff differential equations

AbstractThis paper first discusses the conditions in which a set of differential equations should give stable solutions, starting with linear systems assuming that these do not differ greatly in this respect from non-linear systems. Methods of investigating the stability of particular systems are briefly discussed. Most real biochemical systems are known from observation to be stable, but little is known of the regions over which stability persists; moreover, models of biochemical systems may not be stable, because of inaccurate choice of parameter values.The separate problem of stability and accuracy in numerical methods of approximating the solution of systems of non-linear equations is then treated. Stress is laid on the consistently unsatisfactory results given by explicit methods for systems containing “stiff” equations, and implicit multistep methods are particularly recommended for this class of problem, which is likely to include many biochemical model systems. Finally, an iteration procedure likely to give convergence both in multistep methods and in the steady-state approach is recommended, and areas in which improvement in methods is likely to occur are outlined

The factor VII activating protease G511E (Marburg) variant and cardiovascular risk

A previous study had shown a strong relationship between a variant in factor VII activating protease (FSAP G511E) and advanced carotid atheroma. In-vitro, the variant has reduced fibrinolytic but normal pro-coagulant activity, which may constitute a prothrombotic state. The current study has addressed risk for coronary heart disease in a prospective study of cardio vascular disorders (Northwick Park Heart Study II). An interactive effect upon risk was found between the 511E allele and elevated levels of cholesterol and triglyceride. Fibrinogen could substitute for triglyceride levels in this risk-interaction analysis. The findings support the proposal that the FSAP 511E allele exacerbates atherosclerosis or its clinical sequelae

Increased plasma markers of oxidative stress are associated with coronary heart disease in males with diabetes mellitus and with 10-year risk in a prospective sample of males

Background: Increased oxidative stress is associated with coronary heart disease (CHD). We examined the association between plasma markers of oxidative stress and CHD in a cross-sectional sample of patients with diabetes and prospective CHD risk in a sample of men predominantly without diabetes. Methods: Plasma total antioxidant status (TAOS) and the ratio of oxidized LDL (Ox-LDL) to LDL-cholesterol (LDL-C) were determined in a cross-section of 761 Caucasian individuals with diabetes (UDACS study). Plasma TAOS was also determined in 310 baseline samples from a 10-year prospective cohort of 3012 healthy males (NPHSII). Results: Within UDACS, males with CHD had lower mean (SD) plasma TAOS [no CHD, 43.4 (13.2)%; CHD, 40.3 (13.8)%; P = 0.04]. The prevalence of CHD was higher in the lowest compared with the upper quartiles (32.7% vs 19.7%; P = 0.004). We observed a significant association between plasma Ox-LDL:LDL-C and CHD status [no CHD vs CHD, 16.9 (3.1) vs 19.3 (5.0) units/mmol; P = 0.04], with the prevalence of CHD being higher among men in the upper compared with lower quartiles (18.4% vs 35.1%; P = 0.003). No association was observed in females. In NPHSII, TAOS was lower in those who developed CHD [35.1 (8.0)% vs 37.1 (7.9)%; P = 0.04]. The odds ratio for CHD in the lowest compared with the upper quartile was 1.91 (95% confidence interval, 0.99–3.70; P = 0.04). This remained unchanged after adjustment for classic risk factors. Conclusions: A cross-sectional and prospective association exists between baseline plasma measures of oxidative stress and CHD risk. The association with prospective CHD risk remained after adjustment for "traditional" risk factors, implying an independent role for oxidative stress in CHD risk

Developing an ancient epithelial appendage: FGF signalling regulates early tail denticle formation in sharks

Background: Vertebrate epithelial appendages constitute a diverse group of organs that includes integumentary structures such as reptilian scales, avian feathers and mammalian hair. Recent studies have provided new evidence for the homology of integumentary organ development throughout amniotes, despite their disparate fnal morphologies. These structures develop from conserved molecular signalling centres, known as epithelial placodes. It is not yet certain whether this homology extends beyond the integumentary organs of amniotes, as there is a lack of knowledge regarding their development in basal vertebrates. As the ancient sister lineage of bony vertebrates, extant chondrichthyans are well suited to testing the phylogenetic depth of this homology. Elasmobranchs (sharks, skates and rays) possess hard, mineralised epithelial appendages called odontodes, which include teeth and dermal denticles (placoid scales). Odontodes constitute some of the oldest known vertebrate integumentary appendages, predating the origin of gnathostomes. Here, we used an emerging model shark (Scyliorhinus canicula) to test the hypothesis that denticles are homologous to other placode-derived amniote integumentary organs. To examine the conservation of putative gene regulatory network (GRN) member function, we undertook small molecule inhibition of fbroblast growth factor (FGF) signalling during caudal denticle formation. Results: We show that during early caudal denticle morphogenesis, the shark expresses homologues of conserved developmental gene families, known to comprise a core GRN for early placode morphogenesis in amniotes. This includes conserved expression of FGFs, sonic hedgehog (shh) and bone morphogenetic protein 4 (bmp4). Additionally, we reveal that denticle placodes possess columnar epithelial cells with a reduced rate of proliferation, a conserved characteristic of amniote skin appendage development. Small molecule inhibition of FGF signalling revealed placode development is FGF dependent, and inhibiting FGF activity resulted in downregulation of shh and bmp4 expression, consistent with the expectation from comparison to the amniote integumentary appendage GRN. Conclusion: Overall, these fndings suggest the core GRN for building vertebrate integumentary epithelial appendages has been highly conserved over 450 million years. This provides evidence for the continuous, historical homology of epithelial appendage placodes throughout jawed vertebrates, from sharks to mammals. Epithelial placodes constitute the shared foundation upon which diverse vertebrate integumentary organs have evolved

4f spin density in the reentrant ferromagnet SmMn2Ge2

The spin contribution to the magnetic moment in SmMn2Ge2 has been measured by magnetic Compton scattering in both the low and high temperature ferromagnetic phases. At low temperature, the Sm site is shown to possess a large 4f spin moment of 3.4 +/- 0.1 Bohr magnetons, aligned antiparallel to the total magnetic moment. At high temperature, the data show conclusively that ordered magnetic moments are present on the samarium site.Comment: 5 pages, 2 figures, transferred from PRL to PRB (Rapid Comm.

A quantification of the relationship between neuronal responses in the rat rostral ventromedial medulla and noxious stimulation-evoked withdrawal reflexes

The rostral ventromedial medulla (RVM) regulates a range of involuntary behaviours but is most often associated with nociception via the action of pronociceptive ON cells and antinociceptive OFF cells. The phasic responses of ON and OFF cells determine whether or not incoming noxious signals provoke a withdrawal reflex, and previous studies have suggested that reflex RVM activity patterns actively shape motor output. Here we challenged the model by using juvenile rats, which are known to exhibit markedly different reflex responses compared with adults. By recording single-cell activity in the RVM and the electromyography responses of hindlimb flexor muscles to noxious thermal stimulation we found that the juvenile reflex had a shorter onset latency, was larger in amplitude and exhibited a decreased rise time compared with the adult reflex. The responses of ON and OFF cells faithfully tracked the shorter onset latency of the reflex by also responding earlier and, thus, still preceded the reflex. However, neither the reflex amplitude nor the ongoing response profile was predicted by the firing rate of RVM cells in either age group. Instead we found a close correspondence between RVM activity and the reflex only during the initiation of the response. Furthermore, the short rise time of the juvenile reflex was reflected in higher rates of change of both ON and OFF cell firing. Our data suggest that the RVM is associated only with the initiation of reflexes and does not shape ongoing muscle activity, which is more likely to be subserved by downstream spinal processes

Quantum field dynamics of the slow rollover in the linear delta expansion

We show how the linear delta expansion, as applied to the slow-roll transition in quantum mechanics, can be recast in the closed time-path formalism. This results in simpler, explicit expressions than were obtained in the Schr\"odinger formulation and allows for a straightforward generalization to higher dimensions. Motivated by the success of the method in the quantum-mechanical problem, where it has been shown to give more accurate results for longer than existing alternatives, we apply the linear delta expansion to four-dimensional field theory. At small times all methods agree. At later times, the first-order linear delta expansion is consistently higher that Hartree-Fock, but does not show any sign of a turnover. A turnover emerges in second-order of the method, but the value of $$at the turnover is larger that that given by the Hartree-Fock approximation. Based on this calculation, and our experience in the corresponding quantum-mechanical problem, we believe that the Hartree-Fock approximation does indeed underestimate the value of$$ at the turnover. In subsequent applications of the method we hope to implement the calculation in the context of an expanding universe, following the line of earlier calculations by Boyanovsky {\sl et al.}, who used the Hartree-Fock and large-N methods. It seems clear, however, that the method will become unreliable as the system enters the reheating stage.Comment: 17 pages, 9 figures, revised version with extra section 4.2 including second order calculatio

A Grand Canonical Ensemble Approach to the Thermodynamic Properties of the Nucleon in the Quark-Gluon Coupling Model

In this paper, we put forward a way to study the nucleon's thermodynamic properties such as its temperature, entropy and so on, without inputting any free parameters by human hand, even the nucleon's mass and radius. First we use the Lagrangian density of the quark gluon coupling fields to deduce the Dirac Equation of the quarks confined in the gluon fields. By boundary conditions we solve the wave functions and energy eigenvalues of the quarks, and thus get energy-momentum tensor, nucleon mass, and density of states. Then we utilize a hybrid grand canonical ensemble, to generate the temperature and chemical potentials of quarks, antiquarks of three flovars by the four conservation laws of the energy and the valence quark numbers, after which, all other thermodynamic properties are known. The only seemed free paremeter, the nucleon radius is finally determined by the grand potential minimal principle.Comment: 5 pages, LaTe