Abstract: According to Thompson’s principle of similarity, the area of an object should be proportional to its length squared. However, leaf area–length data of some plants have been demonstrated not to follow the principle of similarity. We explore the reasons why the leaf area–length allometry deviates from the principle of similarity and examine whether there is a general model describing the relationship among leaf area, width and length. We sampled more than 11,800 leaves from six classes of woody and herbaceous plants and tested the leaf area–length allometry. We compared six mathematical models based on root-mean-square error as the measure of goodness-of-fit. The best supported model described a proportional relationship between leaf area and the product of leaf width and length (i.e., the Montgomery model). We found that the extent to which the leaf area–length allometry deviates from the principle of similarity depends upon the extent of variation of the ratio of leaf width to length. Estimates of the parameter of the Montgomery model ranged between 1/2, which corresponds to a triangular leaf with leaf length as its height and leaf width as its base, and π/4, which corresponds to an elliptical leaf with leaf length as its major axis and leaf width as its minor axis, for the six classes of plants. The narrow range in practice of the Montgomery parameter implies an evolutionary stability for the leaf area of large-leaved plants despite the fact that leaf shapes of these plants are rather different.

Abstract: Although many fruit geometries resemble a solid of revolution, this assumption has rarely been rigorously examined. To test this assumption, 574 fruits of Canarium album (Lour.) DC. which appear to have an ellipsoidal shape, were examined to determine the validity of a general avian-based egg-shape equation, referred to as the explicit Preston equation (EPE). The assumption that the C. album fruit geometry is a solid of revolution is tested by applying the volume formula for a solid of revolution using the EPE. The goodness of fit of the EPE was assessed using the adjusted root-mean-square error (RMSEadj). The relationship between the observed volume (Vobs) of each fruit, as measured by water displacement in a graduated cylinder, and the predicted volumes (Vpre) based on the EPE was also evaluated using the equation Vpre = slope * Vobs. All the RMSEadj values were smaller than 0.05, which demonstrated the validity of the EPE based on C. album fruit profiles. The 95% confidence interval of the slope of Vpre vs. Vobs included 1.0, indicating that there was no significant difference between Vpre and Vobs. The data confirm that C. album fruits are solids of revolution. This study provides a new approach for calculating the volume and surface area of geometrically similar fruits, which can be extended to other species with similar fruit geometries to further explore the ontogeny and evolution of angiosperm reproductive organs.

Abstract: Delve into the diverse aspects of plant morphology, their responses to global climate change, and the spatiotemporal dynamics of forest productivity. Join us on a journey through the intricate web of plant characteristics and their impact on the environment.

Abstract: During the past decades, the poration of cell membrane induced by pulsed electric fields has been widely investigated. Since the basic mechanisms of this process have not yet been fully clarified, many research activities are focused on the development of suitable theoretical and numerical models. To this end, a nonlinear, nonlocal, dispersive, and space-time numerical algorithm has been developed and adopted to evaluate the transmembrane voltage and pore density along the perimeter of realistic irregularly shaped cells. The presented model is based on the Maxwell's equations and the asymptotic Smoluchowski's equation describing the pore dynamics. The dielectric dispersion of the media forming the cell has been modeled by using a general multirelaxation Debye-based formulation. The irregular shape of the cell is described by using the Gielis' superformula. Different test cases pertaining to red blood cells, muscular cells, cell in mitosis phase, and cancer-like cell have been investigated. For each type of cell, the influence of the relevant shape, the dielectric properties, and the external electric pulse characteristics on the electroporation process has been analyzed. The numerical results demonstrate that the proposed model is an efficient numerical tool to study the electroporation problem in arbitrary-shaped cells.

Abstract: Electromagnetic design problems involve optimizing multiple parameters that are nonlinearly related to objective functions. Traditional optimization techniques require significant computational resources that grow exponentially as the problem size increases. Therefore, a method that can produce good results with moderate memory and computational resources is desirable. Bioinspired optimization methods, such as particle swarm optimization (PSO), are known for their computational efficiency and are commonly used in various scientific and technological fields. In this article we explore the potential of advanced PSO-based algorithms to tackle challenging electromagnetic design and analysis problems faced in real-life applications. It provides a detailed comparison between conventional PSO and its quantum-inspired version regarding accuracy and computational costs. Additionally, theoretical insights on convergence issues and sensitivity analysis on parameters influencing the stochastic process are reported. The utilization of a novel quantum PSO-based algorithm in advanced scenarios, such as reconfigurable and shaped lens antenna synthesis, is illustrated. The hybrid modeling approach, based on the unified geometrical description enabled by the Gielis Transformation, is applied in combination with a suitable quantum PSO-based algorithm, along with a geometrical tube tracing and physical optics technique for solving the inverse problem aimed at identifying the geometrical parameters that yield optimal antenna performance.

Abstract: Electroporation technique is widely used in biotechnology and medicine for the transport of various molecules through the membranes of biological cells. Different mathematical models of electroporation have been proposed in the literature to study pore formation in plasma and nuclear membranes. These studies are mainly based on models using a single isolated cell with a canonical shape. In this work, a spacetime (x,y,t) multiphysics model based on quasi-static Maxwells equations and nonlinear Smoluchowskis equation has been developed to investigate the electroporation phenomenon induced by pulsed electric field in multicellular systems having irregularly shape. The dielectric dispersion of the cell compartments such as nuclear and plasmatic membranes, cytoplasm, nucleoplasm and external medium have been incorporated into the numerical algorithm, too. Moreover, the irregular cell shapes have been modeled by using the Gielis transformations.

Abstract: Generalized Möbius-Listing surfaces and bodies generalize Möbius bands, and this research was motivated originally by solutions of boundary value problems. Analogous to cutting of the original Möbius band, for this class of surfaces and bodies, results have been obtained when cutting such bodies or surfaces. In general, cutting leads to interlinked and intertwined different surfaces or bodies, resulting in very complex systems. However, under certain conditions, the result of cutting can be a single surface or body, which reduces complexity considerably. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin

Abstract: Gielis curves (GC) can represent a wide range of shapes and patterns ranging from star shapes to symmetric and asymmetric polygons, and even self intersecting curves. Such patterns appear in natural objects or phenomena, such as flowers, crystals, pollen structures, animals, or even wave propagation. Gielis curves and surfaces are an extension of Lamé curves and surfaces (superquadrics) which have benefited in the last two decades of extensive researches to retrieve their parameters from various data types, such as range images, 2D and 3D point clouds, etc. Unfortunately, the most efficient techniques for superquadrics recovery, based on deterministic methods, cannot directly be adapted to Gielis curves. Indeed, the different nature of their parameters forbids the use of a unified gradient descent approach, which requires initial pre-processings, such as the symmetry detection, and a reliable pose and scale estimation. Furthermore, even the most recent algorithms in the literature remain extremely sensitive to initialization and often fall into local minima in the presence of large missing data. We present a simple evolutionary algorithm which overcomes most of these issues and unifies all of the required operations into a single though efficient approach. The key ideas in this paper are the replacement of the potential fields used for the cost function (closed form) by the shortest Euclidean distance (SED, iterative approach), the construction of cost functions which minimize the shortest distance as well as the curve length using R-functions, and slight modifications of the evolutionary operators. We show that the proposed cost function based on SED and R-function offers the best compromise in terms of accuracy, robustness to noise, and missing data.

Abstract: Gielis transformations are a generalization of Lame curves. To combine domains, we can make use of the natural alliance between Lame's work and Rvachev's R-functions. A logical next step is the extension to n-valued logic dening dierent partitions.

Abstract: Ginkgo biloba L. is a precious relic tree species with important economic value. Seeds, as a vital reproductive organ of plants, can be used to distinguish cultivars of the species. We chose 400 seeds from two cultivars of ginkgo (Fozhi and Maling; 200 seeds for each cultivar) as the study material and used the Gielis equation to fit the projected shape of these seeds. The coefficients of variation (CV) in root mean squared errors (RMSE) obtained from the fitted data were used to compare the level of inter-cultivar variations in seed shape. We also used the covariance analysis to compare the allometric relationships between seed weights and projected areas of these two cultivars. The Gielis equation fitted well the seed shapes of two ginkgo cultivars. The lower CV in RMSE of cultivar Fozhi than Maling indicated a less symmetrical seed shape in the latter than the former. The bootstrap percentile method showed that the seed shape differences between the two cultivars were significant. However, there was no significant difference in the exponents between the seed weights and the projected areas of these two cultivars. Overall, the significant differences in shapes between the seeds of two ginkgo cultivars were well explained by the Gielis equation; this model can be further extended to compare morphological differences in other ginkgo cultivars, and even for plant seeds or animal eggs that have similar oval shapes.

Abstract: In the present paper we consider the “bulky knots'' and ”bulky links'', which appear after cutting a Generalized Möbius Listing's GMLn3 body (whose radial cross section is a plane 3-symmetric figure with three vertices) along different Generalized Möbius Listing's surfaces GMLn2 situated in it. This article is aimed to investigate the number and geometric structure of the independent objects appearing after such a cutting process of GMLn3 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known tabulation for Knots and Links of small complexity.

Abstract: In this communication, the use of Gielis transformation to design more compact metamaterial unit cells is explored. For this purpose, transformed complementary split ring resonators and spiral resonators are coupled to micro-strip lines and theirbehaviour is investigated. The obtained results confirm that the useof the considered class of supershaped geometries enables the synthesis of very compact scalable microwave components.

Abstract: In this report we describe the basics of biological carbon fixation in bamboo forests. Confusing carbon stock with carbon flux has led to false expectations on the significance of bamboo forests as carbon sinks. Furthermore, misunderstandings about the growth of bamboo culms can lead to highly exaggerated expectations on the productivity of bamboo.

Abstract: In this work, the electroporation phenomenon induced by pulsed electric field on different nucleated biological cells is studied. A nonlinear, non-local, dispersive, and space-time multiphysics model based on Maxwell's and asymptotic Smoluchowski's equations has been developed to calculate the transmembrane voltage and pore density on both plasma and nuclear membrane perimeters. The irregular cell shape has been modeled by incorporating in the numerical algorithm the analytical functions pertaining to Gielis curves. The dielectric dispersion of the cell media has been modeled considering the multi-relaxation Debye-based relationship. Two different irregular nucleated cells have been investigated and their response has been studied applying both the dispersive and non-dispersive models. By a comparison of the obtained results, differences can be highlighted confirming the need to make use of the dispersive model to effectively investigate the cell response in terms of transmembrane voltages, pore densities, and electroporation opening angle, especially when irregular cell shapes and short electric pulses are considered. Bioelectromagnetics. 2019;40:331-342. (c) 2019 Wiley Periodicals, Inc.

Abstract: Many cross-sectional shapes of plants have been found to approximate a superellipse rather than an ellipse. Square bamboos, belonging to the genus Chimonobambusa (Poaceae), are a group of plants with round-edged square-like culm cross sections. The initial application of superellipses to model these culm cross sections has focused on Chimonobambusa quadrangularis (Franceschi) Makino. However, there is a need for large scale empirical data to confirm this hypothesis. In this study, approximately 750 cross sections from 30 culms of C. utilis were scanned to obtain cross-sectional boundary coordinates. A superellipse exhibits a centrosymmetry, but in nature the cross sections of culms usually deviate from a standard circle, ellipse, or superellipse because of the influences of the environment and terrain, resulting in different bending and torsion forces during growth. Thus, more natural cross-sectional shapes appear to have the form of a deformed superellipse. The superellipse equation with a deformation parameter (SEDP) was used to fit boundary data. We find that the cross-sectional shapes (including outer and inner rings) of C. utilis can be well described by SEDP. The adjusted root-mean-square error of SEDP is smaller than that of the superellipse equation without a deformation parameter. A major finding is that the cross-sectional shapes can be divided into two types of superellipse curves: hyperellipses and hypoellipses, even for cross sections from the same culm. There are two proportional relationships between ring area and the product of ring length and width for both the outer and inner rings. The proportionality coefficients are significantly different, as a consequence of the two different superellipse types (i.e., hyperellipses and hypoellipses). The difference in the proportionality coefficients between hyperellipses and hypoellipses for outer rings is greater than that for inner rings. This work informs our understanding and quantifying of the longitudinal deformation of plant stems for future studies to assess the influences of the environment on stem development. This work is also informative for understanding the deviation of natural shapes from a strict rotational symmetry.