Phylogenetic, ecological and intraindividual variability patterns in grass phytolith shape.

BACKGROUND AND AIMS: Grass silica short cell (GSSC) phytoliths appear to be the most reliable source of fossil evidence for tracking the evolutionary history and paleoecology of grasses. In recent years, modern techniques that quantitatively assess phytolith shape variation have widened opportunities for the classification of grass fossil phytoliths. However, phylogenetic, ecological and intraindividual variability patterns in phytolith shape remain largely unexplored. METHODS: The full range of intraindividual phytolith shape variation [3650 two-dimensional (2-D) outlines] from 73 extant grass species, 48 genera, 18 tribes and eight subfamilies (particularly Pooideae) was analysed using geometric morphometric analysis based on semi-landmarks spanning phytolith outlines. KEY RESULTS: The 2-D phytolith shape is mainly driven by deep-time diversification of grass subfamilies. There is distinct phytolith shape variation in early-diverging lineages of Pooideae (Meliceae, Stipeae). The amount of intraindividual variation in phytolith shape varies among species, resulting in a remarkable pattern across grass phylogeny. CONCLUSIONS: The phylogenetic pattern in phytolith shape was successfully revealed by applying geometric morphometrics to 2-D phytolith shape outlines, strengthening the potential of phytoliths to track the evolutionary history and paleoecology of grasses. Geometric morphometrics of 2-D phytolith shape is an excellent tool for analysis requiring large numbers of phytolith outlines, making it useful for quantitative palaeoecological reconstruction.

Inter- and intraspecific variation in grass phytolith shape and size: a geometric morphometrics perspective.

BACKGROUND AND AIMS: The relative contributions of inter- and intraspecific variation to phytolith shape and size have only been investigated in a limited number of studies. However, a detailed understanding of phytolith variation patterns among populations or even within a single plant specimen is of key importance for the correct taxonomic identification of grass taxa in fossil samples and for the reconstruction of vegetation and environmental conditions in the past. In this study, we used geometric morphometric analysis for the quantification of different sources of phytolith shape and size variation. METHODS: We used landmark-based geometric morphometric methods for the analysis of phytolith shapes in two extant grass species (Brachypodium pinnatum and B. sylvaticum). For each species, 1200 phytoliths were analysed from 12 leaves originating from six plants growing in three populations. Phytolith shape and size data were subjected to multivariate Procrustes analysis of variance (ANOVA), multivariate regression, principal component analysis and linear discriminant analysis. KEY RESULTS: Interspecific variation largely outweighed intraspecific variation with respect to phytolith shape. Individual phytolith shapes were classified with 83 % accuracy into their respective species. Conversely, variation in phytolith shapes within species but among populations, possibly related to environmental heterogeneity, was comparatively low. CONCLUSIONS: Our results imply that phytolith shape relatively closely corresponds to the taxonomic identity of closely related grass species. Moreover, our methodological approach, applied here in phytolith analysis for the first time, enabled the quantification and separation of variation that is not related to species discrimination. Our findings strengthen the role of grass phytoliths in the reconstruction of past vegetation dynamics.

Hybrid liquid-membrane lenses made by one fixed and one or two active optical components.

The paper presents a methodology of calculation of the inner structure of two- and three-component hybrid liquid-membrane lenses with variable focal length that have corrected spherical aberration and coma. Specifically, the formulas for calculation of initial-design inner parameters (radii of curvatures of individual surfaces, axial thickness, and refractive indices of a material of the lens) of a thin-lens system are derived for a hybrid two-component system (doublet) made by one glass and one liquid-membrane lens, and a hybrid three-component lens (triplet) made by one glass lens and two liquid-membrane lenses, which both have variable focal length and corrected spherical aberration and coma for an object at infinity. As optimization during the optical design process requires the starting point be very close to the optimal solution, the presented approach can be successfully used for its calculation, as it is based on fundamental proven formulas of optical aberrations.

Calculation of a lens system with one or two aspherical surfaces having corrected spherical aberration.

The paper presents a detailed theoretical analysis of characteristics of a rotationally symmetric lens system with one or two aspherical surfaces having corrected spherical aberration and reduced coma aberration for a given position of the object and the image. Formulas for surface shape optimization are derived, and the procedure for calculating the aspherical system is shown. The presented formulas are verified with examples of ray tracing.

Diffraction by perfect and imperfect amplitude grating.

The paper presents theoretical formulas for calculation of diffraction by perfect infinite and finite amplitude gratings with Fresnel and Fraunhofer approximations. Further, general formulas for diffraction by an imperfect diffraction grating are derived where edges of the grating are described with general harmonic functions. Such a formalism provides enough power to accurately characterize imperfections of diffraction gratings, and it serves as a simple tool for a solution to a diffraction problem.

Design of zoom systems composed of lenses with variable focal length.

This paper develops a methodology for a design of zoom-systems, which are composed of thin optical components with a variable focal length (e.g., membrane lenses). The proposed procedure allows us to design not only the outer parameters of the system (focal lengths and separation of lenses), but the inner structure of individual components of the system can be calculated as well (radii of curvature, thicknesses, and refractive indices) i.e., the starting values of the mentioned parameters can be calculated and used for the next optimization.

Double curvature membrane lens.

The paper presents a theoretical analysis of properties of a specific liquid membrane lens composed of two axially symmetric membranes of different thicknesses and double curvature. These membranes enclose a space where an optical liquid is filled. Mechanical and optical properties of the lens are then changed by varying the volume of the liquid. The paper presents new formulas for calculation of membrane deflections, radii of curvatures of the membranes, and axial geometry, which offer to minimize the third-order spherical aberration of the lens for an object at infinity. The presented theory is examined on specific examples.

Fundamental design parameters of two-component optical systems: theoretical analysis.

The paper presents a detailed theoretical analysis of two-component optical systems of Petzval objective, tele-objectives, reverse tele-objectives, and objectives of anallactic type. This type of optical system is popular in practice, especially in the field of photographic technologies and surveying devices (theodolites, levelling devices, etc.), where anallactic telescopes with inner focusing are used. The paper presents methods of designing of fundamental parameters of the objective, i.e., focal distances of the objective's components and their mutual distance, and radii of curvatures of individual surfaces if the components are cemented doublets. Further, a detailed analysis of aberration properties of those optical systems is presented.

Fundamental characterization of a priori measurement accuracy of terrestrial laser scanning.

This paper summarizes, presents, and derives fundamental formulas and principles of characterization of a priori measurement accuracy of terrestrial laser scanning. The first part is focused on a general mathematical description of geometrical properties of the scanner, and useful general formulas for uncertainty analysis of all types of scanner constructions are presented. Afterwards, a description of physical aspects affecting terrestrial laser scanning follows. The final part of the paper summarizes the presented analysis on examples.

Spherical aberration of an optical system and its influence on depth of focus.

This paper analyzes the influence of spherical aberration on the depth of focus of symmetrical optical systems for imaging of axial points. A calculation of a beam's caustics is discussed using ray equations in the image plane and considering longitudinal spherical aberration as well. Concurrently, the influence of aberration coefficients on extremes of such a curve is presented. Afterwards, conditions for aberration coefficients are derived if the Strehl definition should be the same in two symmetrically placed planes with respect to the paraxial image plane. Such conditions for optical systems with large aberrations are derived with the use of geometric-optical approximation where the gyration diameter of the beam in given planes of the optical system is evaluated. Therefore, one can calculate aberration coefficients in such a way that the optical system generates a beam of rays that has the gyration radius in a given interval smaller than the defined limit value. Moreover, one can calculate the maximal depth of focus of the optical system respecting the aforementioned conditions.

Calculation of nonlinearly deformed membrane shape of liquid lens caused by uniform pressure.

The paper discusses a numerical calculation of deformation of a circular axisymmetric membrane of a liquid lens caused by the pressure of an optical liquid. Since such deflections of the membrane are many times larger than the membrane thickness, a nonlinear model is applied and generalized relationships are derived that characterize the resulting shape with a high precision and permit an accurate analysis of imaging properties of the lens and of optical aberrations. By comparison with experimental data, it is shown that the presented model is suitable to describe the deformation of the membrane of the lens.

Deformation of a prestressed liquid lens membrane.

This paper presents a complete model for analysis of the deformed shape of a prestressed circular axisymmetric membrane of a liquid lens. The governing equations are derived using the exact relation between displacements and the Green-Lagrange strains combined with the Saint Venant-Kirchhoff material law, which postulates a linear relation between the Green-Lagrange strains and the second Piola-Kirchoff stresses. A numerical solution based on minimization of potential energy is illustrated by an example, and the dependence of the maximum membrane deflection on material properties and initial prestress is analyzed. The theoretical model is then experimentally validated. It is shown that the model is suitable for large-strain analysis of liquid lens membranes and provides sufficiently accurate results that can be used in further analyses and simulations of imaging properties of active optical elements based on liquid lenses.

Simple method for determination of parameters of cemented doublet.

This paper proposes a simple noninvasive method that makes it possible to calculate the inner design parameters of the cemented doublet using measurements of its chosen paraxial optical and geometrical parameters without any damage to the system under testing (e.g., dismantling). Derived formulas are based on the knowledge of measured values of the lenses thicknesses, the radii of curvatures of the first and the last doublet's surfaces, the paraxial focal length, and positions of the object and the image focal point. Practical usefulness of the proposed method is demonstrated on the real measurement of a known doublet.

3D optical two-mirror scanner with focus-tunable lens.

The paper presents formulas for a ray tracing in the optical system of two-mirror optical scanner with a focus-tunable lens. Furthermore, equations for the calculation of focal length which ensure focusing of a beam in the desired point in a detection plane are derived. The uncertainty description of such focal length follows as well. The chosen vector approach is general; therefore, the application of formulas in various configurations of the optical systems is possible. In the example situation, the authors derived formulas for mirrors' rotations and the focal length depending on the position of the point in the detection plane.

Use of diffraction grating for measuring the focal length and distortion of optical systems.

The paper presents an experimentally simple, accurate, and inexpensive method for measuring the focal length and distortion of optical systems using a diffraction grating, where both of the properties are determined from the transversal distances of diffraction maximums in one measurement. The proposed approach does not require any special components or any expensive equipment. A detailed theoretical analysis is performed, and the estimation of uncertainties is studied as well. Afterward, the method is demonstrated with a computer simulation and experimental measurement, and compared with commercially available measurement devices. It is shown that the method provides sufficiently accurate results for many practical applications; therefore, it is appropriate for laboratory testing and for industrial applications.

One-mirror and two-mirror three-dimensional optical scanners--position and accuracy of laser beam spot.

This article presents several fundamental formulas for ray tracing in optical systems used in 3D optical scanners. A procedure for numerical modeling of one-mirror and two-mirror optical systems is presented, and the calculation of positioning and accuracy of the laser beam spot in a detection plane is carried out. Finally, a point position and accuracy depending on a transit time is evaluated.

[The role of learning curve on the results of aortic valve implantation for severe aortic stenosis]. / Vliv zkusenosti na výsledky katetrové implantace aortální chlopne v lécbe významné aortální stenózy.

INTRODUCTION: Patients with serious aortic stenoses treated by conservative therapy have significantly worse life expectancy. Besides the surgical aortic valve replacement (AVR) as the gold standard of therapy, the transcatheter aortic valve implantation (TAVI) is indicated in patients at very high risk or who are contraindicated to AVR. The role of learning-curve in TAVI has to be established. AIM: Assessment of the results of consecutive TAVI procedures based on the experience of the team. METHODS: 58 high-risk consecutive patients with the average age of 82.2 years were divided into 3 groups based on the TAVI order ( 20., 21.-40., 41.-58.). After the Edwards SAPIEN implantation via transfemoral or transapical approaches, all patients were followed for minimum 30 days. Data from the national registry (Czech TAVI Registry) were used for the retrospective analysis. Comparison of the groups was done by using the Kruskal-Wallis test, Mann-Whitney U test and χ2 test. RESULTS: Significantly shorter procedural time (p < 0.001), hospitalization (p = 0.033) and a lower amount of contrast medium (p < 0.001) was observed during the time. There was no difference in the rate of clinical complications at 30 days. CONCLUSIONS: Increasing experience of the TAVI implantation team is associated with significantly shorter procedural time, hospitalization and a lower amount of contrast medium. Overall very good clinical results during 30 days were not affected by the team experience.

Hot spring oases in the periglacial desert as the Last Glacial Maximum refugia for temperate trees in Central Europe.

Northern glacial refugia are a hotly debated concept. The idea that many temperate organisms survived the Last Glacial Maximum (LGM; ~26.5 to 19 thousand years) in several sites across central and northern Europe stems from phylogeographic analyses, yet direct fossil evidence has thus far been missing. Here, we present the first unequivocal proof that thermophilous trees such as oak (Quercus), linden (Tilia), and common ash (Fraxinus excelsior) survived the LGM in Central Europe. The persistence of the refugium was promoted by a steady influx of hydrothermal waters that locally maintained a humid and warm microclimate. We reconstructed the geological and palaeohydrological factors responsible for the emergence of hot springs during the LGM and argue that refugia of this type, allowing the long-term survival and rapid post-LGM dispersal of temperate elements, were not exceptional in the European periglacial zone.

The Effect of Addition Potassium Permanganate on Bond Strength of Hot-Dip Galvanized Plain Bars with Cement Paste.

In this paper, the effect of gradually increasing amounts of KMnO4 (10-4, 10-3, 10-2 mol·L-1) in cement paste on the bond strength of a plain hot-dip galvanized steel bar was evaluated. The open-circuit potential of HDG samples in cement paste with various additions of MnO4- was monitored in order to follow a transfer of zinc from activity to passivity. Furthermore, the influence of the addition of these anions on the physicochemical properties of normal-strength concrete or cement paste was evaluated by means of hydration heat measurements, X-ray diffraction analysis, and compressive strength. The effective concentration of MnO4- anions prevents the corrosion of the coating with hydrogen evolution and ensures that the bond strength is not reduced by their action, which was determined to be 10-3 mol·L-1. Lower additions of MnO4- anions (10-4 mol·L-1) are ineffective in this respect. On the other hand, higher additions of MnO4- anions (10-2 mol·L-1), although they ensure the corrosion of the coating in fresh concrete without hydrogen evolution, but affect the hydration process of the cement paste that was demonstrated by slight water separation.