“The Mӧbius phenomenon in Generalized Mӧbius-Listing bodies with cross sections of odd and even polygons”. Gielis J, Tavkhelidze I, Sn –, 1512-0066 34, 23 (2020)
Keywords: A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“The Möbius phenomenon in Generalized Möbius-Listing surfaces and bodies, and Arnold's Cat phenomenon”. Gielis J, Ricci PE, Tavkhelidze I, Advanced Studies : Euro-Tbilisi Mathematical Journal 14, 17 (2021). http://doi.org/10.3251/ASETMJ/1932200812
Abstract: Möbius bands have been studied extensively, mainly in topology. Generalized Möbius-Listing surfaces and bodies providing a full geometrical generalization, is a quite new field, 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. Our research is motivated by this reduction of complexity. In the study of cutting Generalized Möbius-Listing bodies with polygons as cross section, the conditions under which a single body results, displaying the Möbius phenomenon of a one-sided body, have been determined for even and odd polygons. These conditions are based on congruence and rotational symmetry of the resulting cross sections after cutting, and on the knife cutting the origin. The Möbius phenomenon is important, since the process of cutting (or separation of zones in a GML body in general) then results in a single body, not in different, intertwined domains. In all previous works it was assumed that the cross section of the GML bodies is constant, but the main result of this paper is that it is sufficient that only one cross section on the whole GML structure meets the conditions for the Möbius phenomenon to occur. Several examples are given to illustrate this.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3251/ASETMJ/1932200812
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“Modeling in mathematics : proceedings of the second Tbilisi-Salerno workshop on modeling in mathematics”. Gielis J, Ricci PE, Tavkhelidze I page 185 p. (2017).
Keywords: ME3 Book as editor; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8
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“Modeling of electroporation induced by pulsed electric fields in irregularly shaped cells”. Mescia L, Chiapperino MA, Bia P, Gielis J, Caratelli D, IEEE transactions on biomedical engineering 65, 414 (2018). http://doi.org/10.1109/TBME.2017.2771943
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/TBME.2017.2771943
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“Multiphysics modelling of membrane electroporation in irregularly shaped cells”. Mescia L, Chiapperino MA, Bia P, Lamacchia CM, Gielis J, Caratelli D, Progress in Electromagnetic Research Symposium (PIERS)
T2 –, 2019 PhotonIcs &, Electromagnetics Research Symposium –, Spring (PIERS-Spring), 17-20 June 2019, Rome, Italy , 2992 (2019). http://doi.org/10.1109/PIERS-SPRING46901.2019.9017428
Abstract: Electroporation is a non-thermal electromagnetic phenomenon widely used in medical diseases treatment. Different mathematical models of electroporation have been proposed in literature to study pore evolution in biological membranes. This paper presents a nonlinear dispersive multiphysic model of electroporation in irregular shaped biological cells in which the spatial and temporal evolution of the pores size is taken into account. The model solves Maxwell and asymptotic Smoluchowski equations and it describes the dielectric dispersion of cell media using a Debye-based relationship. Furthermore, the irregular cell shape has been modeled using the Gielis superformula. Taking into account the cell in mitosis phase, the electroporation process has been studied comparing the numerical results pertaining the model with variable pore radius with those in which the pore radius is supposed constant. The numerical analysis has been performed exposing the biological cell to a rectangular electric pulse having duration of 10 μs. The obtained numerical results highlight considerable differences between the two different models underling the need to include into the numerical algorithm the differential equation modeling the spatial and time evolution of the pores size.
Keywords: P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/PIERS-SPRING46901.2019.9017428
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“Nonlinear dispersive model of electroporation for irregular nucleated cells”. Chiapperino MA, Bia P, Caratelli D, Gielis J, Mescia L, Dermol-Cerne J, Miklavcic D, Bioelectromagnetics 40, 331 (2019). http://doi.org/10.1002/BEM.22197
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.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1002/BEM.22197
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“A note about generalized forms of the Gielis formula”. Gielis J, Natalini P, Ricci PE page 107 (2017).
Abstract: We generalize the Gielis Superformula by extending the R. Chacon approach, but avoiding the use of Jacobi elliptic functions. The obtained results are extended to the three-dimensional case. Several new shapes are derived by using the computer algebra system Mathematica(C).
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_8
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“On a geometric model of bodies with “complex” configuration and some movements”. Tavkhelidze I, Caratelli D, Gielis J, Ricci PE, Rogava M, Transirico M page 129 (2017).
Abstract: Aim of this chapter is analytical representation of one wide class of geometric figures (lines, surfaces and bodies) and their complicated displacements. The accurate estimation of physical characteristics (such as volume, surface area, length, or other specific parameters) relevant to human organs is of fundamental importance in medicine. One central idea of this article is, in this respect, to provide a general methodology for the evaluation, as a function of time, of the volume and center of gravity featured by moving of one class of bodies used of describe different human organs.
Keywords: H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_10
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“On means, polynomials and special functions”. Gielis J, Verhulst R, Caratelli D, Ricci PE, Tavkhelidze I, The teaching of mathematics 17, 1 (2014)
Keywords: A1 Journal article; Educational sciences; Sustainable Energy, Air and Water Technology (DuEL)
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“Phi-bonacci in Ancient Greece”. Gielis J, Symmetry : culture and science 32, 25 (2021). http://doi.org/10.26830/SYMMETRY_2021_1_025
Abstract: Fibonacci numbers are a very popular subject in mathematics, culture and science. A major open question is why the ancient Greeks overlooked this series, while they were very familiar with the golden mean and division in extreme and mean ratio. Furthermore, they could compute the square root of five to a high degree of precision using Theon 's ladder. This fact is based on tables built with side and diagonal numbers, and it is a simple and incredibly efficient method to compute roots of integers, though it is little known even now among most of the experts. The biologist D 'Arcy Wentworth Thompson showed that the same method could be used to generate the Fibonacci series using a simple shift in the computation of the tables. He argues, quite convincingly, that the ancient Greeks could not have overlooked this. Actually, the same method can be used to generate all possible regular phyllotaxis patterns.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_1_025
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“Potential fields of self intersecting Gielis curves for modeling and generalized blending techniques”. Fougerolle Y, Truchetet F, Gielis J, Modeling In Mathematics 2, 67 (2017). http://doi.org/10.2991/978-94-6239-261-8_6
Abstract: The definition of Gielis curves allows for the representation of self intersecting curves. The analysis and the understanding of these representations is of major interest for the analytical representation of sectors bounded by multiple subsets of curves (or surfaces), as this occurs for instance in many natural objects. We present a construction scheme based on R-functions to build signed potential fields with guaranteed differential properties, such that their zero-set corresponds to the outer, the inner envelop, or combined subparts of the curve. Our framework is designed to allow for the definition of composed domains built upon Boolean operations between several distinct objects or some subpart of self-intersecting curves, but also provides a representation for soft blending techniques in which the traditional Boolean union and intersection become special cases of linear combinations between the objects' potential fields. Finally, by establishing a connection between R-functions and Lame curves, we can extend the domain of the p parameter within the R-p-function from the set of the even positive numbers to the real numbers strictly greater than 1, i.e. p is an element of]1, +infinity[.
Keywords: P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.2991/978-94-6239-261-8_6
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“Proceedings of the 9th World Bamboo Congress, Antwerp 2012”. Gielis J, Potters G, (2012)
Keywords: P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“The process of cutting GMLmn bodies with dm-knives”. Tavkhelidze I, Gielis J, Sn –, 1512-0066 32, 67 (2018)
Keywords: A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
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“Proportional relationship between leaf area and the product of leaf length and width of four types of special leaf shapes”. Shi P, Liu M, Yu X, Gielis J, Ratkowsky DA, Forests (19994907) 10, 178 (2019). http://doi.org/10.3390/F10020178
Abstract: The leaf area, as an important leaf functional trait, is thought to be related to leaf length and width. Our recent study showed that the Montgomery equation, which assumes that leaf area is proportional to the product of leaf length and width, applied to different leaf shapes, and the coefficient of proportionality (namely the Montgomery parameter) range from 1/2 to π/4. However, no relevant geometrical evidence has previously been provided to support the above findings. Here, four types of representative leaf shapes (the elliptical, sectorial, linear, and triangular shapes) were studied. We derived the range of the estimate of the Montgomery parameter for every type. For the elliptical and triangular leaf shapes, the estimates are π/4 and 1/2, respectively; for the linear leaf shape, especially for the plants of Poaceae that can be described by the simplified Gielis equation, the estimate ranges from 0.6795 to π/4; for the sectorial leaf shape, the estimate ranges from 1/2 to π/4. The estimates based on the observations of actual leaves support the above theoretical results. The results obtained here show that the coefficient of proportionality of leaf area versus the product of leaf length and width only varies in a small range, maintaining the allometric relationship for leaf area and thereby suggesting that the proportional relationship between leaf area and the product of leaf length and width broadly remains stable during leaf evolution.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/F10020178
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“Relevance of the cell membrane modelling for accurate analysis of the pulsed electric field-induced electroporation”. Mescia L, Chiapperino MA, Bia P, Lamacchia CM, Gielis J, Caratelli D, Progress in Electromagnetic Research Symposium (PIERS)
T2 –, 2019 PhotonIcs &, Electromagnetics Research Symposium –, Spring (PIERS-Spring), 17-20 June 2019, Rome, Italy , 2985 (2019). http://doi.org/10.1109/PIERS-SPRING46901.2019.9017456
Abstract: In this work, a nonlinear dispersive multiphysic model based on Maxwell and asymptotic Smoluchowsky equations has been developed to analyze the electroporation phenomenon induced by pulsed electric field on biological cells. The irregular plasma membrane geometry has been modeled by incorporating in the numerical algorithm the Gielis superformula as well as the dielectric dispersion of the plasma membrane has been modeled using the multi-relaxation Debye-based relationship. The study has been carried out with the aim to compare our model implementing a thin plasma membrane with the simplified model in which the plasma membrane is modeled as a distributed impedance boundary condition. The numerical analysis has been performed exposing the cell to external electric pulses having rectangular shapes. By an inspection of the obtained results, significant differences can be highlighted between the two models confirming the need to incorporate the effective thin membrane into the numerical algorithm to well predict the cell response to the pulsed electric fields in terms of transmembrane voltages and pore densities, especially when the cell is exposed to external nanosecond pulses.
Keywords: P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1109/PIERS-SPRING46901.2019.9017456
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“A robust evolutionary algorithm for the recovery of rational Gielis curves”. Fougerolle YD, Truchetet F, Demonceaux C, Gielis J, Pattern recognition 46, 2078 (2013). http://doi.org/10.1016/J.PATCOG.2013.01.024
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.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1016/J.PATCOG.2013.01.024
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“The scaling relationships of leaf biomass vs. leaf surface area of 12 bamboo species”. Huang W, Su X, Ratkowsky DA, Niklas KJ, Gielis J, Shi P, Global ecology and conservation 20, e00793 (2019). http://doi.org/10.1016/J.GECCO.2019.E00793
Abstract: There is convincing evidence for a scaling relationship between leaf dry weight (DW) and leaf surface area (A) for broad-leaved plants, and most estimates of the scaling exponent of DW vs. A are greater than unity. However, the scaling relationship of leaf fresh weight (FW) vs. A has been largely neglected. In the present study, we examined whether there is a statistically strong scaling relationship between FW and A and compared the goodness of fit to that of DW vs. A. Between 250 and 520 leaves from each of 12 bamboo species within 2 genera (Phyllostachys and Pleioblastus) were investigated. The reduced major axis regression protocols were used to determine scaling relationships. The fit for the linearized scaling relationship of FW vs. A was compared with that of DW vs. A using the coefficient of determination (i.e., r2). A stronger scaling relationship between FW and A than that between DW and A was observed for each of the 12 bamboo species investigated. Among the 12 species examined, five had significantly smaller scaling exponents of FW vs. A compared to those of DW vs. A; only one species had a scaling exponent of FW vs. A greater than that of DW vs. A. No significant difference between the two scaling exponents was observed for the remaining 6 species. Researchers conducting future studies might be well advised to consider the influence of leaf fresh weight when exploring the scaling relationships of foliar biomass allocation patterns.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1016/J.GECCO.2019.E00793
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“Some properties of “bulky&rdquo, links, generated by Generalized Möbius Listing's bodies GML4n”. Caratelli D, Gielis J, Ricci PE, Tavkhelidze I, Journal of mathematical sciences 216, 509 (2016). http://doi.org/10.1007/S10958-016-2907-X
Abstract: In the present paper, we consider the bulky knots and bulky links that appear after cutting of generalized MöbiusListing GML 4 n bodies (with corresponding radial cross sections square) along different generalized MöbiusListing surfaces GML 2 n situated in it. The aim of this article is to examine the number and geometric structure of independent objects that appear after such a cutting process of GML 4 n 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.
Keywords: A2 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1007/S10958-016-2907-X
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“Some properties of “bulky&rdquo, links, generated by Generalized Möbius Listing's bodies GML4n”. Caratelli D, Gielis J, Ricci PE, Tavkhelidze I, (2013)
Keywords: P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“Spherical harmonic solution of the Robin problem for the Helmholtz equation in a supershaped shell”. Caratelli D, Gielis J, Tavkhelidze I, Ricci PE, Applied mathematics 4, 263 (2013). http://doi.org/10.4236/AM.2013.41A040
Abstract: The Robin problem for the Helmholtz equation in normal-polar shells is addressed by using a suitable spherical harmonic expansion technique. Attention is in particular focused on the wide class of domains whose boundaries are defined by a generalized version of the so-called superformula introduced by Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica? is developed in order to validate the proposed methodology. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.4236/AM.2013.41A040
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“Structure of the dm knives and process of cutting of GML(man) or GRT(man) bodies”. Tavkhelidze I, Gielis J, Sn –, 1512-0066 33 (2019)
Keywords: A3 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“Temperate bamboos in ornamental horticulture: differentiators and spillover effects into the 21st century”. Gielis J page 603 (2012).
Keywords: H3 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“The apeirogon and dual numbers”. Gielis J, Brasili S, Symmetry : culture and science 32, 157 (2021). http://doi.org/10.26830/SYMMETRY_2021_2_157
Abstract: The richness, diversity, connection, depth and pleasure of studying symmetry continue to open doors. Here we report a connection between Coxeter's Apeirogon and the geometry associated with pictorial space, parabolic rotation and dual numbers.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2021_2_157
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“The Robin problem for the Helmholtz equation in a starlike planar domain”. Caratelli D, Gielis J, Natalini P, Ricci PE, Tavkhelidze I, Georgian mathematical journal 18, 465 (2011). http://doi.org/10.1515/GMJ.2011.0031
Abstract: The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are defined by the so-called superformula introduced by J. Gielis. A dedicated numerical procedure based on the computer algebra system Mathematica© is developed in order to validate the proposed approach. In this way, highly accurate approximations of the solution, featuring properties similar to the classical ones, are obtained. The computed results are found to be in good agreement with the theoretical findings on Fourier series expansion presented by L. Carleson.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1515/GMJ.2011.0031
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“Towards a geometrical theory of morphology and morphogenesis”. Gielis J, Ding Y, Shi P, (2016)
Keywords: P3 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
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“Universal natural shapes : from unifying shape description to simple methods for shape analysis and boundary value problems”. Gielis J, Caratelli D, Fougerolle Y, Ricci PE, Tavkelidze I, Gerats T, PLoS ONE 7, e29324 (2012). http://doi.org/10.1371/JOURNAL.PONE.0029324
Abstract: Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.1371/JOURNAL.PONE.0029324
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“Why does not the leaf weight-area allometry of bamboos follow the 3/2-power law?”.Lin S, Shao L, Hui C, Song Y, Reddy GVP, Gielis J, Li F, Ding Y, Wei Q, Shi P, Reddy GVP, Frontiers in plant science 9, 583 (2018). http://doi.org/10.3389/FPLS.2018.00583
Abstract: The principle of similarity (Thompson, 1917) states that the weight of an organism follows the 3/2-power law of its surface area and is proportional to its volume on the condition that the density is constant. However, the allometric relationship between leaf weight and leaf area has been reported to greatly deviate from the 3/2-power law, with the irregularity of leaf density largely ignored for explaining this deviation. Here, we choose 11 bamboo species to explore the allometric relationships among leaf area (A), density (ρ), length (L), thickness (T), and weight (W). Because the edge of a bamboo leaf follows a simplified two-parameter Gielis equation, we could show that A ∝ L2 and that A ∝ T2. This then allowed us to derive the density-thickness allometry ρ ∝ Tb and the weight-area allometry W ∝ A(b+3)/2 ≈ A9/8, where b approximates −3/4. Leaf density is strikingly negatively associated with leaf thickness, and it is this inverse relationship that results in the weight-area allometry to deviate from the 3/2-power law. In conclusion, although plants are prone to invest less dry mass and thus produce thinner leaves when the leaf area is sufficient for photosynthesis, such leaf thinning needs to be accompanied with elevated density to ensure structural stability. The findings provide the insights on the evolutionary clue about the biomass investment and output of photosynthetic organs of plants. Because of the importance of leaves, plants could have enhanced the ratio of dry material per unit area of leaf in order to increase the efficiency of photosynthesis, relative the other parts of plants. Although the conclusion is drawn only based on 11 bamboo species, it should also be applicable to the other plants, especially considering previous works on the exponent of the weight-area relationship being less than 3/2 in plants.
Keywords: A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3389/FPLS.2018.00583
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Gielis J (2023) Fred Van Oystaeyen : Time hybrids: a new generic theory of reality. 347–351
Keywords: Review; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.26830/SYMMETRY_2023_3_357
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“Inequality measure of leaf area distribution for a drought-tolerant landscape plant”. Huang L, Ratkowsky DA, Hui C, Gielis J, Lian M, Shi P, Plants 12, 3143 (2023). http://doi.org/10.3390/PLANTS12173143
Abstract: Measuring the inequality of leaf area distribution per plant (ILAD) can provide a useful tool for quantifying the influences of intra- and interspecific competition, foraging behavior of herbivores, and environmental stress on plants’ above-ground architectural structures and survival strategies. Despite its importance, there has been limited research on this issue. This paper aims to fill this gap by comparing four inequality indices to measure ILAD, using indices for quantifying household income that are commonly used in economics, including the Gini index (which is based on the Lorenz curve), the coefficient of variation, the Theil index, and the mean log deviation index. We measured the area of all leaves for 240 individual plants of the species Shibataea chinensis Nakai, a drought-tolerant landscape plant found in southern China. A three-parameter performance equation was fitted to observations of the cumulative proportion of leaf area vs. the cumulative proportion of leaves per plant to calculate the Gini index for each individual specimen of S. chinensis. The performance equation was demonstrated to be valid in describing the rotated and right shifted Lorenz curve, given that >96% of root-mean-square error values were smaller than 0.004 for 240 individual plants. By examining the correlation between any of the six possible pairs of indices among the Gini index, the coefficient of variation, the Theil index, and the mean log deviation index, the data show that these indices are closely related and can be used interchangeably to quantify ILAD.
Keywords: A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3390/PLANTS12173143
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“Leaf functional traits : ecological and evolutionary implications”. Shi P, Gielis J, Niklas KJ, Niinemets Ü, Schrader J page 185 p. (2023).
Keywords: ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL)
DOI: 10.3389/978-2-83252-086-4
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