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Stability of neuronal pulses composed of concatenated unstable kinks.

We demonstrate that a traveling pulse solution, emerging from the concatenation of two unstable kinks, can be stable. By means of stability analysis and numerical simulations, we show the stability of neuronal pulses (action potentials) with increasing refractory periods, which decompose into two (radiationally) unstable kinks in the limit. These action potentials are solutions of an ultrarefractory version of the FitzHugh-Nagumo system.

Action Potentials↗

Hydrodynamics of probabilistic ballistic annihilation.

We consider a dilute gas of hard spheres in dimension d> or =2 that upon collision either annihilate with probability p or undergo an elastic scattering with probability 1-p . For such a system neither mass, momentum, nor kinetic energy is a conserved quantity. We establish the hydrodynamic equations from the Boltzmann equation description. Within the Chapman-Enskog scheme, we determine the transport coefficients up to Navier-Stokes order, and give the closed set of equations for the hydrodynamic fields chosen for the above coarse-grained description (density, momentum, and kinetic temperature). Linear stability analysis is performed, and the conditions of stability for the local fields are discussed.

Journal Article↗

Chronic low back pain in traumatic lower limb amputees.

OBJECTIVE: To ascertain the prevalence of back pain amongst traumatic lower limb amputees attending a regional rehabilitation centre and to determine the possible causes of back pain. DESIGN: All traumatic lower limb amputees given a semi-structured questionnaire to complete and a comparative subgroup of amputees with back pain and without back pain underwent physical examination, gait analysis, magnetic resonance scanning (MRI) and gait/standing stability analysis. SETTING: A subregional amputee rehabilitation centre. RESULTS: Transfemoral amputees were more likely to suffer from back pain (81 %) than transtibial amputees (62%) (p<0.05) and of those suffering from severe back pain, 89% and 81% also suffered from severe pain in the phantom limb and severe stump pain respectively. In two comparative subgroups of amputees there was no significant difference between back pain and pain-free groups except those with pain were more likely to have a body mass index (BMI) ratio above 50% of the recommended ratio. No difference in degeneration or disc disease between the groups on MR scans was found. Impact ground reaction forces during walking, irrespective of limb, were significantly greater (p < 0.05) in the pain-free group than in the pain group, as was walking speed. Gait asymmetry measures were similar in both groups. Centre of pressure displacement measures during standing were greater in the pain group than in the pain-free group. CONCLUSIONS: Low back pain in amputees is a significant problem equal to that of pain in the phantom limb and a biomechanical (myofascial) rather than a degenerative aetiology is suggested.

Adolescent↗

Instantaneous postural stability characterization using time-frequency analysis.

Postural stability assessment is critical to a more accurate understanding of sway and balance control. The center of pressure (COP) metric has been shown to be a suitable output measure for time and frequency analysis. However, the center of pressure is a non-stationary signal. Standard time and frequency analysis methods may not be adequate for monitoring the dynamic changes in the center of pressure signal. In this study a time-frequency method, based on data-adaptive evolutionary spectral estimation, is applied to monitor the dynamic changes of the center of pressure in a non-stationary environment. Metrics including the instantaneous mean frequency (IMF), instantaneous spectral bandwidth (ISB), and instantaneous average power (IAP) are analyzed to characterize the center of pressure signal in both the anterior-posterior (AP) and the medial-lateral (ML) planes. Within the confines of this study, the IMF was found to be inversely proportional to IAP. The inverse proportionality factors were calculated in both eyes-open and eyes-closed trials during upright quiet standing. These findings suggest that the time-frequency analysis provides instantaneous metrics which describe the amplitude changes and frequency shift of the center of pressure under a variety of environmental conditions, thus providing a more reliable quantification of postural control.

Adult↗

Epistasis in the multiple locus symmetric viability model.

The n-locus two-allele symmetric viability model is considered in terms of the parameters measuring the additive epistasis in fitness. The dynamics is analysed using a simple linear transformation of the gametic frequencies, and then the recurrence equations depend on the epistatic parameters and Geiringer's recombination distribution only. The model exhibits an equilibrium, the central equilibrium, where the 2n gametes are equally frequent. The transformation simplifies the stability analysis of the central point, and provides the stability conditions in terms of the existence conditions of other equilibria. For total negative epistasis (all epistatic parameters are negative) the central point is stable for all recombination distributions. For free recombination either a central point (segregating one, two, ... or n loci) or the n-locus fixation states are stable. For no recombination and some epistatic parameters positive the central point is unstable and several boundary equilibria may be locally stable. The sign structure of the additive epistasis is therefore an important determinant of the dynamics of the n-locus symmetric viability model. The non-symmetric multiple locus models previously analysed are dynamically related, and they all have an epistatic sign structure that resembles that of the multiplicative viability model. A non-symmetric model with total negative epistasis which share dynamical properties with the similar symmetric model is suggested.

Alleles↗

Rupture of thin stagnant films on a solid surface due to random thermal and mechanical perturbations.

A generalized formalism for the rupture of a nondraining thin film on a solid support due to imposed random thermal and mechanical perturbations, modeled as a Gaussian white noise, is presented. The evolution of amplitude of perturbation is described by a stochastic differential equation. The average film rupture time is the average time for the amplitude of perturbation to equal to the film thickness and is calculated by employing a first passage time analysis for different amplitudes of imposed perturbations, wavenumbers, film thickness, van der Waals and electrostatic interactions and surface tensions. The results indicate the existence of an optimum wavenumber at which the rupture time is minimum. A critical film thickness is identified based on the sign of the disjoining pressure gradient, below which the film is unstable in that the rupture time is very small. The calculated values of rupture time as well as the optimum wavenumber in the present analysis agree well with the results of linear stability analysis for immobile as well as completely mobile gas-liquid film interfaces. For stable films, the rupture time is found to increase dramatically with film thickness near the critical film thickness. As expected, the average rupture time was found to be higher for smaller amplitudes of imposed perturbations, larger surface potentials, larger surface tensions and smaller Hamaker constants.

Algorithms↗

Conformational stability of human skeletal tropomyosins modified by site-directed mutagenesis.

We have used human beta-tropomyosin produced in Escherichia coli and deletion mutants obtained by site-directed mutagenesis to analyse the conformational stability of this molecule under various experimental conditions. Protein engineering has allowed us to answer some questions raised by stability analysis of the wild-type tropomyosin. The complex pattern of denaturation is due neither to heterogeneity of the preparation nor to head-to-tail interactions. The N- and C-termini are not of importance for the thermal stability of the molecule. On the contrary, deletion of the 31 C-terminus amino acids leads to a dramatic decrease of the stability observed in guanidinium chloride. This lowering is interpreted as the participation of one more guanidinium chloride ions to the denaturation equilibrium. Analysis of the stability in presence of organic solvents reveals that acetonitrile and methanol induce opposite effects. Investigation of these effects by three methods (CD, fluorescence and electrophoresis that measure respectively the content in alpha-helix, the contact between the two strands and the strands exchange) leads to the conclusion that strand separation can precede the denaturation of the alpha-helix.

Circular Dichroism↗

Pharmacoeconomic analysis of oral therapies for onychomycosis: a US model.

An evaluation of treatment practices in 13 countries, not including the United States, has shown oral terbinafine to be more cost-effective (from a government payer perspective) than griseofulvin, itraconazole, and ketoconazole in the treatment of onychomycosis of toenails and fingernails. The purpose of this study was to evaluate the clinical and economic effects of oral griseofulvin, itraconazole, ketoconazole, and terbinafine in the treatment of onychomycosis from the perspective of a third-party payer in the United States. A previously constructed decision-analytic model evaluating the costs of onychomycosis in 13 countries outside the United States was updated to determine the costs of treating onychomycosis in the United States. Clinical management patterns were assessed to identify and quantify physician visits, laboratory tests, and adverse drug reaction treatment components for patients with toenail and fingernail onychomycosis. A random-effects model meta-analysis of treatment efficacy (mycologic cure) and New York Metropolitan Medicare charge data for physician fees were used in the treatment model. A sensitivity analysis assessing alternative dosing regimens and a rank order stability analysis investigating the effects of length of treatment, success rates, relapse rates, and drug acquisition costs on overall results were also conducted. Terbinafine had the lowest cost per mycologic cure after one treatment regimen for onychomycosis in both toenail and fingernail infections ($791.00 and $454.00, respectively). The costs of treating toenail and fingernail infections were comparatively higher for therapy with itraconazole ($1535.00 and $767.00, respectively), griseofulvin ($2385.00 and $837.00, respectively), and ketoconazole ($10,025.00 and $1512.00, respectively). As a primary treatment choice, terbinafine also had the lowest overall expected cost per patient for both toenail and fingernail infections ($977.00 and $550.00, respectively). Griseofulvin had expected costs ($1543.00 and $822.00, respectively) similar to itraconazole ($1588.00 and $894.00, respectively), whereas ketoconazole was the most expensive primary treatment choice ($2359.00 and $1287.00, respectively). This study demonstrates that terbinafine is an economical and cost-effective treatment for patients with dermatophytic onychomycosis, supporting European and Canadian studies. Except for the rank order of griseofulvin and itraconazole, sensitivity analyses show that these results are fairly stable.

Administration, Oral↗

The potential of small-scale fusion experiments and the Gordon-Taylor equation to predict the suitability of drug/polymer blends for melt extrusion.

The aim of this study was to investigate the use of small-scale fusion experiments and the Gordon-Taylor (GT) equation to predict whether melt extrusion of a drug with an amorphous polymer produces a stable amorphous dispersion with increased drug dissolution. Indomethacin, lacidipine, nifedipine, piroxicam, and tolbutamide were used as poorly soluble drugs. Drug/polyvinylpyrrolidone (PVP) blends were prepared at a 1:1 mass ratio. Small-scale fusion experiments were performed in a differential scanning calorimeter (DSC) and in stainless steel beakers. Extrusion was performed in a Brabender Plasti-corder. The glass transition temperatures Tg were determined by DSC. Taking an average Tg from the DSC melt, beaker melt, and GT equation accurately predicted the extrudate Tg. Physical stability of beaker melt and extrudate samples was tested by X-ray powder diffraction (XRPD) and DSC after storage at 30 degrees C (beaker melt) or 25 degrees C (extrudate) and less than 10%, 60%, and 75% relative humidity, (RH). Beaker melts were amorphous, apart from some residual crystallinity. Extrudates were amorphous after preparation. Except for indomethacin/PVP, which remained amorphous, the crystallinity of beaker melts and extrudates increased only at 75% RH. Recrystallization occurred even when the Tg of the sample was well above the storage temperature. Chemical stability of the beaker melts and extrudates was tested by capillary electrophoresis and high-performance liquid chromatography (HPLC). Stability was slightly improved in the extrudate compared to the beaker melt. In general, the order for rate of dissolution was crystalline drug was less than the physical mixture, which was less than the drug/PVP beaker melt, which was approximately equal to the extrudate. The use of beaker melts allows a conservative estimate of the potential to melt extrude a drug. To predict physical stability, analysis of the Tg must be combined with physical stability experiments.

Algorithms↗

Structure and dynamics of ferroelectric liquid crystal cells exhibiting thresholdless switching.

Surface-stabilized ferroelectric liquid crystal cells are usually bistable, with the spontaneous polarization either up or down, perpendicular to the plane of the cell. In materials with high spontaneous polarization the polarization charge self-interaction leads to a monostable structure that exhibits a thresholdless, "V-shaped" switching of the optical response to an applied voltage. With a model that includes the electrostatic self-energy of the spontaneous polarization, we examine the transition from bistablity to monostability as a function of the polar and nonpolar anchoring energies, the liquid crystal elasticity, and the thickness of the alignment layers. Two bistable and one monostable structures are possible. The bistable state is only obtained when the thickness of the insulating alignment layer and the polar anchoring energy are small, or when the spontaneous polarization is small. From linear stability analysis we get analytical expressions for the limits of stability of the structures. Numerical calculations show that in some ranges of the parameters two structures can coexist. We also present the calculation of the polarization fluctuation modes. The lowest one becomes soft at the continuous transitions among the structures and at the limits of stability.

Journal Article↗

Preconditioned lattice-Boltzmann method for steady flows.

In this paper we propose a preconditioned lattice Boltzmann (LB) method for steady incompressible flows. For steady flows, the macroscopic equations derived from this LB model are equivalent to those from the standard LB model, but with an improved eigenvalue system. The proposed model can be viewed as an explicit solver for preconditioned compressible Navier-Stokes equations. Linear stability analysis is performed and the results show that the stability of the model is the same as that of the standard LB model for low Mach numbers. The proposed model retains the structure of the standard LB model and, hence, possesses all the advantages. Numerical tests show that the convergence rate can be enhanced as much as an order of magnitude compared to the standard lattice Boltzmann method. The accuracy of the solutions is improved as well.

Journal Article↗

Effects of constant electric fields on the buoyant stability of reaction fronts.

The effects that applying constant electric fields have on the buoyant instability of reaction fronts propagating vertically in a Hele-Shaw cell are investigated for a range of electric field strengths and fluid parameters. The reaction produces a decrease in density across the front such that upwards propagating fronts are buoyantly unstable in the field-free situation. The reaction kinetics are modeled by cubic autocatalysis. A linear stability analysis reveals that a positive electric field increases the stability of a reaction front and can stabilize an otherwise unstable front. A negative field has the opposite effect, making the reaction front more unstable. Numerical simulations of the full nonlinear problem confirm these predictions and show the development of cellular fingers on unstable fronts. These simulations show that the electric field effects on the reaction within the front can alter the fluid density so as to give the possibility of destabilizing an otherwise stable downward propagating front.

Journal Article↗

The stability and persistence of mutualisms embedded in community interactions.

In this paper we argue that two-species models of mutualism may be oversimplifications of the real world that lead to erroneous predictions. We present a four-species model of a pollination mutualism embedded in other types of community interactions. Conclusions derived from two-species models about the destabilizing effect of mutualisms are misleading when applied to the present scenario; although the mutualisms are locally destabilizing, the effect is more than canceled by an increased chance of feasibility. The crucial difference is the interaction of the mutualists with other species in a larger web. Furthermore, community persistence (without unrealistic population explosion), arguably a superior ecological criterion, is greatly enhanced by the presence of mutualisms. Therefore, we predict that mutualisms should be common in the real world, a prediction matching empirial findings and in contrast to the predictions from local stability analysis of basic two-species models. This method of stabilizing a mutualism appears superior in some ways to the often-used method of introducing density dependence in the strength of the mutualism, because it permits obligate mutualisms to exist even at low densities, again matching empirical findings. Lastly, this study is an example of how complex model assemblages can behave qualitatively differently from analogous simpler ones.

Animals↗

Analysis of biochemical phase shift oscillators by a harmonic balancing technique.

The use of harmonic balancing techniques for theoretically investigating a large class of biochemical phase shift oscillators is outlined and the accuracy of this approximate technique for large dimension nonlinear chemical systems is considered. It is concluded that for the equations under study these techniques can be successfully employed to both find periodic solutions and to indicate those cases which can not oscillate. The technique is a general one and it is possible to state a step by step procedure for its application. It has a substantial advantage in producing results which are immediately valid for arbitrary dimension. As the accuracy of the method increases with dimension, it complements classical small dimension methods. The results obtained by harmonic balancing analysis are compared with those obtained by studying the local stability properties of the singular points of the differential equation. A general theorem is derived which identifies those special cases where the results of first order harmonic balancing are identical to those of local stability analysis, and a necessary condition for this equivalence is derived. As a concrete example, the n-dimensional Goodwin oscillator is considered where p, the Hill coefficient of the feedback metabolite, is equal to three and four. It is shown that for p = 3 or 4 and n less than or equal to 4 the approximation indicates that it is impossible to construct a set of physically permissible reaction constants such that the system possesses a periodic solution. However for n greater than or equal to 5 it is always possible to find a large domain in the reaction constant space giving stable oscillations. A means of constructing such a parameter set is given. The results obtained here are compared with previously derived results for p = 1 and p = 2.

Metabolism↗

Chaos synchronization based on a continuous chaos control method in semiconductor lasers with optical feedback.

Chaos synchronization using a continuous chaos control method was studied in two identical chaotic laser systems consisting of semiconductor lasers and optical feedback from an external mirror. Numerical calculations for rate equations indicate that the stability of chaos synchronization depends significantly on the external mirror position. We performed a linear stability analysis for the rate equations. Our results show that the stability of the synchronization is much influenced by the mode interaction between the relaxation oscillation frequency of the semiconductor laser and the external cavity frequency. Due to this interaction, an intensive mode competition between the two frequencies destroys the synchronization, but stable synchronization can be achieved when the mode competition is very weak.

Journal Article↗

Instability criteria and pattern formation in the complex Ginzburg-Landau equation with higher-order terms.

We study the modulational instability and spatial pattern formation in extended media, taking the one-dimensional complex Ginzburg-Landau equation with higher-order terms as a perturbation of the nonlinear Schrödinger equation as a model. By stability analysis for the original partial differential equation, we derive its stability condition as well as the threshold for amplitude perturbations and we show how nonlinear higher-order terms qualitatively change the behavior of the system. The analytical results are found to be in agreement with numerical findings. Modulational instability mediates pattern formation through the lattice. The main feature of the traveling plane waves is its disintegration in pulse train during the propagation through the system.

Journal Article↗

Front and pulse solutions for the complex Ginzburg-Landau equation with higher-order terms.

We investigate one-dimensional complex Ginzburg-Landau equation with higher-order terms and discuss their influences on the multiplicity of solutions. An exact analytic front solution is presented. By stability analysis for the original partial differential equation, we derive its necessary stability condition for amplitude perturbations. This condition together with the exact front solution determine the region of parameter space where the uniformly translating front solution can exist. In addition, stable pulses, chaotic pulses, and attenuation pulses appear generally if the parameters are out of the range. Finally, applying these analysis into the optical transmission system numerically we find that the stable transmission of optical pulses can be achieved if the parameters are appropriately chosen.

Journal Article↗

Field-induced instabilities in two-component systems: the cell-free glycolytic system.

The effects of weak static electric field on a cell-free glycolytic system, which is known to exhibit oscillatory behavior, have been studied using an allosteric model (due to Goldbeter and Lefever). Linear stability analysis is used to determine the change in the nature of stability and the consequent appearance of dissipative structures, due to the electric field. The results show that for this system all the necessary conditions for a field induced instability are satisfied. An order of magnitude calculation of the field strength shows that field strength in the range 10-100 V/cm is required to produce observable change in the system's behavior.

Cell-Free System↗