Using numerical approximation as an intermediate step in analytical derivations: some observations from biomechanics

We present four examples to illustrate the use of a type of numerical approximation as an intermediate step in analytical derivation of seemingly complicated biomechanical equations. The method involves examination of curve shapes to elucidate useful underlying trends, which may otherwise be overlooked through consideration of only the equations themselves. Two examples of the method's use are drawn from recently published results in the area of experimental methods in biomechanics of very soft tissues, and two others are taken from our current work on cartilage tissue mechanics. We think that such observations provide a useful means of circumventing complexity issues when deriving models for biomechanical analysis, and further that the method, while simple in concept, could be effective in a range of biomechanics applications.     

Syntaxonomy of the Robinia pseudoacacia communities in the central peri-adriatic sector of the Italian peninsula

This study presents the results of a floristic vegetational study on Robinia pseudoacacia neoformation forests in the peri-Adriatic sector of central Italy. This has allowed the characterization of these coenoses at the ecological, biogeographic, syntaxonomic and landscape levels. These currently represent the southernmost syntaxa of the Robinietea class described for the Italian peninsula, and the first syntaxonomic contribution of this class in Europe for the Mediterranean biogeographical region. We propose here the new alliance Lauro nobilis–Robinion pseudoacaciae of the order Chelidonio–Robinietalia pseudoacaciae and class Robinietea, with two new associations: Melisso altissimae–Robinietum pseudoacaciae and Rubio peregrinae–Robinietum pseudoacaciae. The new alliance Lauro nobilis–Robinion pseudoacaciae (typus: Melisso altissimae–Robinietum pseudoacaciae) brings together neoformation forests and pre-forest dominated by R. pseudoacacia in those territories with a Mediterranean macroclimate of the peri-Adriatic sector of central Italy. The optimum is found for the alluvial plain and low-slope morphologies, on soils that are moist and rich in organic matter and in areas with anthropic disturbance. On the basis of comparisons with the European context, the alliance Bryonio–Robinion described for the temperate territories of northern Italy is here validated.     

A robust method to estimate the largest Lyapunov exponent of noisy signals: A revision to the Rosenstein’s algorithm

This study proposed a revision to the Rosenstein’s method of numerical calculation of the largest Lyapunov exponent (LyE) to make it more robust to noise. To this aim, the effect of increasing number of initial neighboring points on the LyE value was investigated and compared to values obtained by filtering the time series. Both simulated (Lorenz and passive dynamic walker) and experimental (human walking) time series were used to calculate the LyE. The number of initial neighbors used to calculate LyE for all time series was 1 (the original Rosenstein’s method), 2, 3, 4, 5, 10, 15, 20, 25, and 30 data points. The results demonstrated that the LyE graph reached a plateau at the 15-point neighboring condition implying that the LyE values calculated using at least 15 neighboring points were consistent. The proposed method could be used to calculate more consistent LyE values in experimental time series acquired from biological systems where noise is omnipresent.     

Numerical simulation of birch pollen dispersion with an operational weather forecast system

We included a parameterisation of the emissions of pollen grains into the comprehensive model system COSMO-ART. In addition, a detailed density distribution of birch trees within Switzerland was derived. Based on these new developments, we carried out numerical simulations of the dispersion of pollen grains for an episode that occurred in April 2006 over Switzerland and the adjacent regions. Since COSMO-ART is based on the operational forecast model of the German Weather Service, we are presenting a feasibility study of daily pollen forecast based on methods which have been developed during the last two decades for the treatment of anthropogenic aerosol. A comparison of the model results and very detailed pollen counts documents the current possibilities and the shortcomings of the method and gives hints for necessary improvements.     

A finite volume method for stochastic integrate-and-fire models

The stochastic integrate and fire neuron is one of the most commonly used stochastic models in neuroscience. Although some cases are analytically tractable, a full analysis typically calls for numerical simulations. We present a fast and accurate finite volume method to approximate the solution of the associated Fokker-Planck equation. The discretization of the boundary conditions offers a particular challenge, as standard operator splitting approaches cannot be applied without modification. We demonstrate the method using stationary and time dependent inputs, and compare them with Monte Carlo simulations. Such simulations are relatively easy to implement, but can suffer from convergence difficulties and long run times. In comparison, our method offers improved accuracy, and decreases computation times by several orders of magnitude. The method can easily be extended to two and three dimensional Fokker-Planck equations.

New syntaxonomic contribution to the Vegetation Prodrome of Italy

New syntaxa of different hierarchical levels are here described in order to update the “Syntaxonomic checklist of the Italian classes, orders and alliances (Vegetation Prodrome of Italy)”, promoted in 2012 by the “Ministry of Environment, Land and Sea Protection” in collaboration with the “Italian Society of Botany”. The new alliances, suballiances and associations belong to the Salici purpureae-Populetea nigrae and Querco roboris-Fagetea sylvaticae classes.     

Limiting the sedimentation coefficient for sedimentation velocity data analysis: partial boundary modeling and g(s) approaches revisited

Brown and coworkers (Eur. Biophys. J. 38 (2009) 1079–1099) introduced partial boundary modeling (PBM) to simplify sedimentation velocity data analysis by excluding species outside the range of interest (e.g., aggregates, impurities) via restricting the sedimentation coefficient range being fitted. They strongly criticized the alternate approach of fitting g(s^∗) distributions using similar range limits, arguing that (i) it produces “nonoptimal fits in the original data space” and (ii) the g(s^∗) data transformations lead to gross underestimates of the parameter confidence intervals. It is shown here that neither of those criticisms is valid. These two approaches are not truly fitting the same data or in equivalent ways; thus, they should not actually give the same best-fit parameters. The confidence limits for g(s^∗) fits derived using F statistics, bootstrap, or a new Monte Carlo algorithm are in good agreement and show no evidence for significant statistical distortion. Here 15 g(s^∗) measurements on monoclonal antibody samples gave monomer mass estimates with experimental standard deviations of less than 1%, close to the confidence limit estimates. Tests on both real and simulated data help to clarify the strengths and drawbacks of both approaches. New algorithms for computing g(s^∗) and a scan-differencing approach for PBM are introduced.     

Improved methods for fitting sedimentation coefficient distributions derived by time-derivative techniques

Time-derivative approaches to analyzing sedimentation velocity data have proven to be highly successful and have now been used routinely for more than a decade. For samples containing a small number of noninteracting species, the sedimentation coefficient distribution function, g(s *), traditionally has been fitted by Gaussian functions to derive the concentration, sedimentation coefficient, and diffusion coefficient of each species. However, the accuracy obtained by that approach is limited, even for noise-free data, and becomes even more compromised as more scans are included in the analysis to improve the signal/noise ratio (because the time span of the data becomes too large). Two new methods are described to correct for the effects of long time spans: one approach that uses a Taylor series expansion to correct the theoretical function and a second approach that creates theoretical g(s *) curves from Lamm equation models of the boundaries. With this second approach, the accuracy of the fitted parameters is approximately 0.1% and becomes essentially independent of the time span; therefore, it is possible to obtain much higher signal/noise when needed. This second approach is also compared with other current methods of analyzing sedimentation velocity data.     

Classification of Bacteria and Archaea: Past,present and future

The late 19th century was the beginning of bacterial taxonomy and bacteria were classified on the basis of phenotypic markers. The distinction of prokaryotes and eukaryotes was introduced in the 1960s. Numerical taxonomy improved phenotypic identification but provided little information on the phylogenetic relationships of prokaryotes. Later on, chemotaxonomic and genotypic methods were widely used for a more satisfactory classification. Archaea were first classified as a separate group of prokaryotes in 1977. The current classification of Bacteria and Archaea is based on an operational-based model, the so-called polyphasic approach, comprised of phenotypic, chemotaxonomic and genotypic data, as well as phylogenetic information. The provisional status Candidatus has been established for describing uncultured prokaryotic cells for which their phylogenetic relationship has been determined and their authenticity revealed by in situ probing.