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	Author	Gielis, J.; Caratelli, D.; Fougerolle, Y.; Ricci, P.E.; Gerats, T.
	Title	A biogeometrical model for corolla fusion in Asclepiad flowers			Type	H1 Book chapter
	Year	2017	Publication		Abbreviated Journal
	Volume	2	Issue		Pages	83-105 T2 - Modeling in mathematics : proceedings
	Keywords	H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The molecular genetics of flower development have been studied extensively for more than two decades. Fusion of organs and the tendency to oligomery, important characteristics of flower evolution, so far have remained fairly elusive. We present a geometric model for shape and fusion in the corolla of Asclepiads. Examples demonstrate how fusion of petals creates stable centers, a prerequisite for the formation of complex pollination structures via congenital and postgenital fusion events, with the formation of de novo organs, specific to Asclepiads. The development of the corolla reduces to simple inequalities from the MATHS-BOX. The formation of stable centers and of bell and tubular shapes in flowers are immediate and logical consequences of the shape. Our model shows that any study on flowers, especially in evo-devo perspective should be performed within the wider framework of polymery and oligomery and of fusion and synorganization.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400007	Publication Date	2017-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1	Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144551			Serial	7561
Permanent link to this record



	Author	Shi, P.; Ratkowsky, D.A.; Li, Y.; Zhang, L.; Lin, S.; Gielis, J.
	Title	A general leaf area geometric formula exists for plants evidence from the simplified Gielis equation			Type	A1 Journal article
	Year	2018	Publication	Forests (19994907)	Abbreviated Journal
	Volume	9	Issue	11	Pages	714
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Plant leaves exhibit diverse shapes that enable them to utilize a light resource maximally. If there were a general parametric model that could be used to calculate leaf area for different leaf shapes, it would help to elucidate the adaptive evolutional link among plants with the same or similar leaf shapes. We propose a simplified version of the original Gielis equation (SGE), which was developed to describe a variety of object shapes ranging from a droplet to an arbitrary polygon. We used this equation to fit the leaf profiles of 53 species (among which, 48 bamboo plants, 5 woody plants, and 10 geographical populations of a woody plant), totaling 3310 leaves. A third parameter (namely, the floating ratio c in leaf length) was introduced to account for the case when the theoretical leaf length deviates from the observed leaf length. For most datasets, the estimates of c were greater than zero but less than 10%, indicating that the leaf length predicted by the SGE was usually smaller than the actual length. However, the predicted leaf areas approximated their actual values after considering the floating ratios in leaf length. For most datasets, the mean percent errors of leaf areas were lower than 6%, except for a pooled dataset with 42 bamboo species. For the elliptical, lanceolate, linear, obovate, and ovate shapes, although the SGE did not fit the leaf edge perfectly, after adjusting the parameter c, there were small deviations of the predicted leaf areas from the actual values. This illustrates that leaves with different shapes might have similar functional features for photosynthesis, since the leaf areas can be described by the same equation. The anisotropy expressed as a difference in leaf shape for some plants might be an adaptive response to enable them to adapt to different habitats.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000451310300054	Publication Date	2018-11-21
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1999-4907	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:156324			Serial	7389
Permanent link to this record



	Author	Lian, M.; Shi, P.; Zhang, L.; Yao, W.; Gielis, J.; Niklas, K.J.
	Title	A generalized performance equation and its application in measuring the Gini index of leaf size inequality			Type	A1 Journal article
	Year	2023	Publication	Trees: structure and function	Abbreviated Journal
	Volume	37	Issue		Pages	1555-1565
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The goal of this study is to provide a rigorous tool to quantify the inequality of the leaf size distribution of an individual plant, thereby serving as a reference trait for quantifying plant adaptations to local environmental conditions. The tool to be presented and tested employs three components: (1) a performance equation (PE), which can produce flexible asymmetrical and symmetrical bell-shaped curves, (2) the Lorenz curve (i.e., the cumulative proportion of leaf size vs. the cumulative proportion of number of leaves), which is the basis for calculating, and (3) the Gini index, which measures the inequality of leaf size distribution. We sampled 12 individual plants of a dwarf bamboo and measured the area and dry mass of each leaf of each plant. We then developed a generalized performance equation (GPE) of which the PE is a special case and fitted the Lorenz curve to leaf size distribution using the GPE and PE. The GPE performed better than the PE in fitting the Lorenz curve. We compared the Gini index of leaf area distribution with that of leaf dry mass distribution and found that there was a significant difference between the two indices that might emerge from the scaling relationship between leaf dry mass and area. Nevertheless, there was a strong correlation between the two Gini indices (r2 = 0.9846). This study provides a promising tool based on the GPE for quantifying the inequality of leaf size distributions across individual plants and can be used to quantify plant adaptations to local environmental conditions.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001069570200001	Publication Date	2023-08-26
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0931-1890; 1432-2285	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.3	Times cited		Open Access	Not_Open_Access: Available from 26.02.2024
	Notes				Approved	Most recent IF: 2.3; 2023 IF: 1.842
	Call Number	UA @ admin @ c:irua:199562			Serial	8874
Permanent link to this record



	Author	Lin, S.; Zhang, L.; Reddy, G.V.P.; Hui, C.; Gielis, J.; Ding, Y.; Shi, P.
	Title	A geometrical model for testing bilateral symmetry of bamboo leaf with a simplified Gielis equation			Type	A1 Journal article
	Year	2016	Publication	Ecology and evolution	Abbreviated Journal
	Volume	6	Issue	19	Pages	6798-6806
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The size and shape of plant leaves change with growth, and an accurate description of leaf shape is crucial for describing plant morphogenesis and development. Bilateral symmetry, which has been widely observed but poorly examined, occurs in both dicot and monocot leaves, including all nominated bamboo species (approximately 1,300 species), of which at least 500 are found in China. Although there are apparent differences in leaf size among bamboo species due to genetic and environmental profiles, bamboo leaves have bilateral symmetry with parallel venation and appear similar across species. Here, we investigate whether the shape of bamboo leaves can be accurately described by a simplified Gielis equation, which consists of only two parameters (leaf length and shape) and produces a perfect bilateral shape. To test the applicability of this equation and the occurrence of bilateral symmetry, we first measured the leaf length of 42 bamboo species, examining >500 leaves per species. We then scanned 30 leaves per species that had approximately the same length as the median leaf length for that species. The leaf-shape data from scanned profiles were fitted to the simplified Gielis equation. Results confirmed that the equation fits the leaf-shape data extremely well, with the coefficients of determination being 0.995 on average. We further demonstrated the bilateral symmetry of bamboo leaves, with a clearly defined leaf-shape parameter of all 42 bamboo species investigated ranging from 0.02 to 0.1. This results in a simple and reliable tool for precise determination of bamboo species, with applications in forestry, ecology, and taxonomy.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000385626100003	Publication Date	2016-09-02
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2045-7758	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144547			Serial	7998
Permanent link to this record



	Author	Shi, P.; Wang, L.; Quinn, B.K.K.; Gielis, J.
	Title	A new program to estimate the parameters of Preston's equation, a general formula for describing the egg shape of birds			Type	A1 Journal article
	Year	2023	Publication	Symmetry	Abbreviated Journal	Symmetry-Basel
	Volume	15	Issue	1	Pages	231-10
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Preston's equation is a general model describing the egg shape of birds. The parameters of Preston's equation are usually estimated after re-expressing it as the Todd-Smart equation and scaling the egg's actual length to two. This method assumes that the straight line through the two points on an egg's profile separated by the maximum distance (i.e., the longest axis of an egg's profile) is the mid-line. It hypothesizes that the photographed egg's profile is perfectly bilaterally symmetrical, which seldom holds true because of photographic errors and placement errors. The existing parameter estimation method for Preston's equation considers an angle of deviation for the longest axis of an egg's profile from the mid-line, which decreases prediction errors to a certain degree. Nevertheless, this method cannot provide an accurate estimate of the coordinates of the egg's center, and it leads to sub-optimal parameter estimation. Thus, it is better to account for the possible asymmetry between the two sides of an egg's profile along its mid-line when fitting egg-shape data. In this paper, we propose a method based on the optimization algorithm (optimPE) to fit egg-shape data and better estimate the parameters of Preston's equation by automatically searching for the optimal mid-line of an egg's profile and testing its validity using profiles of 59 bird eggs spanning a wide range of existing egg shapes. We further compared this method with the existing one based on multiple linear regression (lmPE). This study demonstrated the ability of the optimPE method to estimate numerical values of the parameters of Preston's equation and provide the theoretical egg length (i.e., the distance between two ends of the mid-line of an egg's profile) and the egg's maximum breadth. This provides a valuable approach for comparing egg shapes among conspecifics or across different species, or even different classes (e.g., birds and reptiles), in future investigations.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000927531000001	Publication Date	2023-01-13
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2073-8994	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.7	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 2.7; 2023 IF: 1.457
	Call Number	UA @ admin @ c:irua:195347			Serial	7279
Permanent link to this record



	Author	Gielis, J.; Natalini, P.; Ricci, P.E.
	Title	A note about generalized forms of the Gielis formula			Type	H1 Book chapter
	Year	2017	Publication		Abbreviated Journal
	Volume	2	Issue		Pages	107-116 T2 - Modeling in mathematics : proceedings
	Keywords	H1 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	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).
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000442076400008	Publication Date	2017-04-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-94-6239-260-1; 978-94-6239-261-8; 2543-0300; 978-94-6239-260-1	Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:144550			Serial	8318
Permanent link to this record



	Author	Gielis, J.; Tavkhelidze, I.
	Title	A note on Generalized Möbius-Listing Bodies			Type	P1 Proceeding
	Year	2023	Publication		Abbreviated Journal
	Volume		Issue		Pages	31-39 T2 - Proceedings of the 1st International Sy
	Keywords	P1 Proceeding; Sustainable Energy, Air and Water Technology (DuEL)
	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
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2023-11-29
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	978-90-833839-0-3	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:201047			Serial	9063
Permanent link to this record



	Author	Gielis, J.; Caratelli, D.; Shi, P.; Ricci, P.E.
	Title	A note on spirals and curvature			Type	A1 Journal article
	Year	2020	Publication	Growth and form	Abbreviated Journal
	Volume	1	Issue	1	Pages	1-8
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Starting from logarithmic, sinusoidal and power spirals, it is shown how these spirals are connected directly with Chebyshev polynomials, Lamé curves, with allometry and Antonelli-metrics in Finsler geometry. Curvature is a crucial concept in geometry both for closed curves and equiangular spirals, and allowed Dillen to give a general definition of spirals. Many natural shapes can be described as a combination of one of two basic shapes in nature—circle and spiral—with Gielis transformations. Using this idea, shape description itself is used to develop a novel approach to anisotropic curvature in nature. Various examples are discussed, including fusion in flowers and its connection to the recently described pseudo-Chebyshev functions.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2020-02-23
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:167061			Serial	6569
Permanent link to this record



	Author	Fougerolle, Y.D.; Truchetet, F.; Demonceaux, C.; Gielis, J.
	Title	A robust evolutionary algorithm for the recovery of rational Gielis curves			Type	A1 Journal article
	Year	2013	Publication	Pattern recognition	Abbreviated Journal
	Volume	46	Issue	8	Pages	2078-2091
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000317944800002	Publication Date	2013-01-29
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0031-3203	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:107181			Serial	8485
Permanent link to this record



	Author	Shi, P.; Chen, L.; Quinn, B.K.; Yu, K.; Miao, Q.; Guo, X.; Lian, M.; Gielis, J.; Niklas, K.J.
	Title	A simple way to calculate the volume and surface area of avian eggs			Type	A1 Journal article
	Year	2023	Publication	Annals of the New York Academy of Sciences	Abbreviated Journal
	Volume	1524	Issue	1	Pages	118-131
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Egg geometry can be described using Preston's equation, which has seldom been used to calculate egg volume (V) and surface area (S) to explore S versus V scaling relationships. Herein, we provide an explicit re-expression of Preston's equation (designated as EPE) to calculate V and S, assuming that an egg is a solid of revolution. The side (longitudinal) profiles of 2221 eggs of six avian species were digitized, and the EPE was used to describe each egg profile. The volumes of 486 eggs from two avian species predicted by the EPE were compared with those obtained using water displacement in graduated cylinders. There was no significant difference in V using the two methods, which verified the utility of the EPE and the hypothesis that eggs are solids of revolution. The data also indicated that V is proportional to the product of egg length (L) and maximum width (W) squared. A 2/3-power scaling relationship between S and V for each species was observed, that is, S is proportional to (LW2)(2/3). These results can be extended to describe the shapes of the eggs of other species to study the evolution of avian (and perhaps reptilian) eggs.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000975679400001	Publication Date	2023-04-28
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0077-8923; 1749-6632	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	5.2	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 5.2; 2023 IF: 4.706
	Call Number	UA @ admin @ c:irua:196724			Serial	8827
Permanent link to this record



	Author	Huang, W.; Li, Y.; Niklas, K.J.; Gielis, J.; Ding, Y.; Cao, L.; Shi, P.
	Title	A superellipse with deformation and its application in describing the cross-sectional shapes of a square bamboo			Type	A1 Journal article
	Year	2020	Publication	Symmetry-Basel	Abbreviated Journal	Symmetry-Basel
	Volume	12	Issue	12	Pages	2073
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000602546300001	Publication Date	2020-12-15
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2073-8994	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	2.7	Times cited		Open Access
	Notes				Approved	Most recent IF: 2.7; 2020 IF: 1.457
	Call Number	UA @ admin @ c:irua:174472			Serial	8622
Permanent link to this record



	Author	Gielis, J.; Tavkhelidze, I.; Ricci, P.E.
	Title	About “bulky” links generated by generalized Möbius-Listing bodies GML₂ⁿ			Type	A2 Journal article
	Year	2013	Publication	Journal of mathematical sciences	Abbreviated Journal
	Volume	193	Issue	3	Pages	449-460
	Keywords	A2 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	In this paper, we consider the bulky knots and bulky links, which appear after cutting of a Generalized MöbiusListing GMLn2 body (with the radial cross section a convex plane 2-symmetric figure with two vertices) along a different Generalized MöbiusListing surfaces GMLn2 situated in it. The aim of this report is to investigate the number and geometric structure of the independent objects that appear after such a cutting process of GMLn2 bodies. In most cases we are able to count the indices of the resulting mathematical objects according to the known classification for the standard knots and links.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2013-08-03
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1072-3374; 1573-8795	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:110953			Serial	7404
Permanent link to this record



	Author	Tavkhelidze, I.; Cassisa, C.; Gielis, J.; Ricci, P.E.
	Title	About “bulky” links, generated by generalized Möbius Listing's bodies GML₃ⁿ			Type	A1 Journal article
	Year	2013	Publication	Matematica e applicazioni : atti della Accademia nazionale dei Lincei	Abbreviated Journal
	Volume	24	Issue	1	Pages	11-38
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000316567700002	Publication Date	2013-03-13
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1120-6357	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:107174			Serial	7405
Permanent link to this record



	Author	Gielis, J.; Tavkelidze, I.; Ricci, P.E.
	Title	About “bulky” links, generated by generalized Möbius-Listing bodies			Type	H3 Book chapter
	Year	2011	Publication		Abbreviated Journal
	Volume		Issue		Pages	115-128 T2 - Proceedings of the International Conf
	Keywords	H3 Book chapter; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-9941-0-3727-6	Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:97753			Serial	7403
Permanent link to this record



	Author	Tavkhelidze, I.; Gielis, J.; Pinelas, S.
	Title	About some methods of analytic representation and classification of a wide set of geometric figures with “complex” configuration			Type	A3 Journal article
	Year	2020	Publication	Sn – 1512-0066	Abbreviated Journal
	Volume	34	Issue		Pages	81-84
	Keywords	A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:174475			Serial	7406
Permanent link to this record



	Author	Tavkhelidze, I.; Gielis, J.; Pinelas, S.
	Title	About some methods of analytic representation and classification of a wide set of geometric figures with “complex” configuration			Type	H1 Book chapter
	Year	2020	Publication		Abbreviated Journal
	Volume		Issue		Pages	347-359 T2 - Differential and difference equations
	Keywords	H1 Book chapter; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2020-10-21
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-3-030-56322-6	Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:174479			Serial	7407
Permanent link to this record



	Author	Mescia, L.; Bia, P.; Gielis, J.; Caratelli, D.
	Title	Advanced particle swarm optimization methods for electromagnetics			Type	P1 Proceeding
	Year	2023	Publication		Abbreviated Journal
	Volume		Issue		Pages	109-122 T2 - Proceedings of the 1st International
	Keywords	P1 Proceeding; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2023-11-29
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	978-90-833839-0-3	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:201048			Serial	9002
Permanent link to this record



	Author	Li, Y.; Niklas, K.J.; Gielis, J.; Niinemets, Ü.; Schrader, J.; Wang, R.; Shi, P.
	Title	An elliptical blade is not a true ellipse, but a superellipse : evidence from two Michelia species			Type	A1 Journal article
	Year	2022	Publication	Journal of forestry research	Abbreviated Journal	J Forestry Res
	Volume	33	Issue	4	Pages	1341-1348
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The shape of leaf laminae exhibits considerable diversity and complexity that reflects adaptations to environmental factors such as ambient light and precipitation as well as phyletic legacy. Many leaves appear to be elliptical which may represent a ‘default’ developmental condition. However, whether their geometry truly conforms to the ellipse equation (EE), i.e., (x/a)2 + (y/b)2 = 1, remains conjectural. One alternative is described by the superellipse equation (SE), a generalized version of EE, i.e., \|x/a\|n +\|y/b\|n = 1. To test the efficacy of EE versus SE to describe leaf geometry, the leaf shapes of two Michelia species (i.e., M. cavaleriei var. platypetala, and M. maudiae), were investigated using 60 leaves from each species. Analysis shows that the majority of leaves (118 out of 120) had adjusted root-mean-square errors of < 0.05 for the nonlinear fitting of SE to leaf geometry, i.e., the mean absolute deviation from the polar point to leaf marginal points was smaller than 5% of the radius of a hypothesized circle with its area equaling leaf area. The estimates of n for the two species were ˂ 2, indicating that all sampled leaves conformed to SE and not to EE. This study confirms the existence of SE in leaves, linking this to its potential functional advantages, particularly the possible influence of leaf shape on hydraulic conductance.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000695118600001	Publication Date	2021-09-12
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1007-662x; 1993-0607	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	3	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 3
	Call Number	UA @ admin @ c:irua:180967			Serial	7152
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	Author	Bia, P.; Caratelli, D.; Mescia, L.; Gielis, J.
	Title	Analysis and synthesis of supershaped dielectric lens antennas			Type	A1 Journal article
	Year	2015	Publication	IET microwaves, antennas and propagation	Abbreviated Journal
	Volume	9	Issue	14	Pages	1497-1504
	Keywords	A1 Journal article; Engineering sciences. Technology; Mass communications; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	A novel class of supershaped dielectric lens antennas, whose geometry is described by the three-dimensional (3D) Gielis formula, is introduced and analysed. To this end, a hybrid modelling approach based on geometrical and physical optics is adopted in order to efficiently analyse the multiple wave reflections occurring within the lens and to evaluate the relevant impact on the radiation properties of the antenna under analysis. The developed modelling procedure has been validated by comparison with numerical results already reported in the literature and, afterwards, applied to the electromagnetic characterisation of Gielis dielectric lens antennas with shaped radiation pattern. Furthermore, a dedicated optimisation algorithm based on quantum particle swarm optimisation has been developed for the synthesis of 3D supershaped lens antennas with single feed, as well as with beamforming capabilities.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000364491200002	Publication Date	2015-08-14
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1751-8725	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:128659			Serial	7441
Permanent link to this record



	Author	de Jong van Coevorden, C.M.; Gielis, J.; Caratelli, D.
	Title	Application of Gielis transformation to the design of metamaterial structures			Type	A1 Journal article
	Year	2018	Publication	Journal of physics : conference series	Abbreviated Journal
	Volume	963	Issue		Pages	Unsp 012008
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000435022800008	Publication Date	2018-02-20
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1742-6588; 1742-6596	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:150947			Serial	7475
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	Author	Gielis, J.; Caratelli, D.; Tavkelidze, I.; Fougerolle, Y.; Ricci, P.E.; Gerats, T.
	Title	Bulky knots and links generated by cutting generalized Mobius-Listing bodies and applications in the natural sciences			Type	H2 Book chapter
	Year	2013	Publication		Abbreviated Journal
	Volume		Issue		Pages	167-183 T2 - Math Art Summit : Koninklijke Vlaamse
	Keywords	H2 Book chapter; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN	978-90-6569-119-4	Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:110955			Serial	7569
Permanent link to this record



	Author	Shi, P.; Yu, K.; Niinemets, Ü.; Gielis, J.
	Title	Can leaf shape be represented by the ratio of leaf width to length? Evidence from nine species of Magnolia and Michelia (Magnoliaceae)			Type	A1 Journal article
	Year	2021	Publication	Forests	Abbreviated Journal	Forests
	Volume	12	Issue	1	Pages	41
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Leaf shape is closely related to economics of leaf support and leaf functions, including light interception, water use, and CO2 uptake, so correct quantification of leaf shape is helpful for studies of leaf structure/function relationships. There are some extant indices for quantifying leaf shape, including the leaf width/length ratio (W/L), leaf shape fractal dimension (FD), leaf dissection index, leaf roundness index, standardized bilateral symmetrical index, etc. W/L ratio is the simplest to calculate, and recent studies have shown the importance of the W/L ratio in explaining the scaling exponent of leaf dry mass vs. leaf surface area and that of leaf surface area vs. leaf length. Nevertheless, whether the W/L ratio could reflect sufficient geometrical information of leaf shape has been not tested. The FD might be the most accurate measure for the complexity of leaf shape because it can characterize the extent of the self-similarity and other planar geometrical features of leaf shape. However, it is unknown how strongly different indices of leaf shape complexity correlate with each other, especially whether W/L ratio and FD are highly correlated. In this study, the leaves of nine Magnoliaceae species (>140 leaves for each species) were chosen for the study. We calculated the FD value for each leaf using the box-counting approach, and measured leaf fresh mass, surface area, perimeter, length, and width. We found that FD is significantly correlated to the W/L ratio and leaf length. However, the correlation between FD and the W/L ratio was far stronger than that between FD and leaf length for each of the nine species. There were no strong correlations between FD and other leaf characteristics, including leaf area, ratio of leaf perimeter to area, fresh mass, ratio of leaf fresh mass to area, and leaf roundness index. Given the strong correlation between FD and W/L, we suggest that the simpler index, W/L ratio, can provide sufficient information of leaf shape for similarly-shaped leaves. Future studies are needed to characterize the relationships among FD and W/L in leaves with strongly varying shape, e.g., in highly dissected leaves.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000611074700001	Publication Date	2020-12-31
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1999-4907	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	1.951	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 1.951
	Call Number	UA @ admin @ c:irua:174473			Serial	7572
Permanent link to this record



	Author	Düking, R.; Gielis, J.; Liese, W.
	Title	Carbon flux and carbon stock in a bamboo stand and their relevance for mitigating climate change			Type	A3 Journal article
	Year	2011	Publication	Bamboo Science & Culture	Abbreviated Journal
	Volume	24	Issue	1	Pages	1-6
	Keywords	A3 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1535-7635	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:91091			Serial	7578
Permanent link to this record



	Author	Shi, P.; Gielis, J.; Niklas, K.J.
	Title	Comparison of a universal (but complex) model for avian egg shape with a simpler model			Type	Editorial
	Year	2022	Publication	Annals of the New York Academy of Sciences	Abbreviated Journal	Ann Ny Acad Sci
	Volume	1514	Issue	1	Pages	34-42
	Keywords	Editorial; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Recently, a universal equation by Narushin, Romanov, and Griffin (hereafter, the NRGE) was proposed to describe the shape of avian eggs. While NRGE can simulate the shape of spherical, ellipsoidal, ovoidal, and pyriform eggs, its predictions were not tested against actual data. Here, we tested the validity of the NRGE by fitting actual data of egg shapes and compared this with the predictions of our simpler model for egg shape (hereafter, the SGE). The eggs of nine bird species were sampled for this purpose. NRGE was found to fit the empirical data of egg shape well, but it did not define the egg length axis (i.e., the rotational symmetric axis), which significantly affected the prediction accuracy. The egg length axis under the NRGE is defined as the maximum distance between two points on the scanned perimeter of the egg's shape. In contrast, the SGE fitted the empirical data better, and had a smaller root-mean-square error than the NRGE for each of the nine eggs. Based on its mathematical simplicity and goodness-of-fit, the SGE appears to be a reliable and useful model for describing egg shape.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000803394100001	Publication Date	2022-06-01
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	0077-8923; 1749-6632	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	5.2	Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: 5.2
	Call Number	UA @ admin @ c:irua:188470			Serial	7139
Permanent link to this record



	Author	Shi, P.-J.; Xu, Q.; Sandhu, H.S.; Gielis, J.; Ding, Y.-L.; Li, H.-R.; Dong, X.-B.
	Title	Comparison of dwarf bamboos (Indocalamus sp.) leaf parameters to determine relationship between spatial density of plants and total leaf area per plant			Type	A1 Journal article
	Year	2015	Publication	Ecology and evolution	Abbreviated Journal
	Volume	5	Issue	20	Pages	4578-4589
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	The relationship between spatial density and size of plants is an important topic in plant ecology. The self-thinning rule suggests a −3/2 power between average biomass and density or a −1/2 power between stand yield and density. However, the self-thinning rule based on total leaf area per plant and density of plants has been neglected presumably because of the lack of a method that can accurately estimate the total leaf area per plant. We aimed to find the relationship between spatial density of plants and total leaf area per plant. We also attempted to provide a novel model for accurately describing the leaf shape of bamboos. We proposed a simplified Gielis equation with only two parameters to describe the leaf shape of bamboos one model parameter represented the overall ratio of leaf width to leaf length. Using this method, we compared some leaf parameters (leaf shape, number of leaves per plant, ratio of total leaf weight to aboveground weight per plant, and total leaf area per plant) of four bamboo species of genus Indocalamus Nakai (I. pedalis (Keng) P.C. Keng, I. pumilus Q.H. Dai and C.F. Keng, I. barbatus McClure, and I. victorialis P.C. Keng). We also explored the possible correlation between spatial density and total leaf area per plant using log-linear regression. We found that the simplified Gielis equation fit the leaf shape of four bamboo species very well. Although all these four species belonged to the same genus, there were still significant differences in leaf shape. Significant differences also existed in leaf area per plant, ratio of leaf weight to aboveground weight per plant, and leaf length. In addition, we found that the total leaf area per plant decreased with increased spatial density. Therefore, we directly demonstrated the self-thinning rule to improve light interception.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000363731500008	Publication Date	2015-09-30
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2045-7758	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:128662			Serial	7691
Permanent link to this record



	Author	Tian, F.; Wang, Y.; Sandhu, H.S.; Gielis, J.; Shi, P.
	Title	Comparison of seed morphology of two ginkgo cultivars			Type	A1 Journal article
	Year	2020	Publication	Journal Of Forestry Research	Abbreviated Journal	J Forestry Res
	Volume	31	Issue	3	Pages	751-758
	Keywords	A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL)
	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.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000529367600005	Publication Date	2018-07-28
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	1007-662x	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor	3	Times cited	3	Open Access
	Notes	; ;			Approved	Most recent IF: 3; 2020 IF: 0.774
	Call Number	UA @ admin @ c:irua:154987			Serial	6474
Permanent link to this record



	Author	Yao, W.; Hui, C.; Wang, L.; Wang, J.; Gielis, J.; Shi, P.
	Title	Comparison of the performance of two polar equations in describing the geometries of elliptical fruits			Type	A1 Journal article
	Year	2024	Publication	Botany letters	Abbreviated Journal
	Volume		Issue		Pages
	Keywords	A1 Journal article; Antwerp engineering, PhotoElectroChemistry & Sensing (A-PECS)
	Abstract	In nature, the two-dimensional (2D) profiles of fruits from many plants often resemble ellipses. However, it remains unclear whether these profiles strictly adhere to the ellipse equation, as many natural shapes resembling ellipses are actually better described as superellipses. The superellipse equation, which includes an additional parameter n compared to the ellipse equation, can generate a broader range of shapes, with the ellipse being just a special case of the superellipse. To investigate whether the 2D profiles of fruits are better described by ellipses or superellipses, we collected a total of 751 mature and undamaged fruits from 31 naturally growing plants of Cucumis melo L. var. agrestis Naud. Our analysis revealed that most adjusted root-mean-square errors (> 92% of the 751 fruits) for fitting the superellipse equation to the fruit profiles were consistently less than 0.0165. Furthermore, there were 638 of the 751 fruits (ca. 85%) with the 95% confidence intervals of the estimated parameter n in the superellipse equation not including 2. These findings suggest that the profiles of C. melo var. agrestis fruits align more closely with the superellipse equation than with the ellipse equation. This study provides evidence for the existence of the superellipse in fruit profiles, which has significant implications for studying fruit geometries and estimating fruit volumes using the solid of revolution formula. Furthermore, this discovery may contribute to a deeper understanding of the mechanisms driving the evolution of fruit shapes.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	001219634500001	Publication Date	2024-05-08
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2381-8107; 2381-8115	ISBN		Additional Links	UA library record; WoS full record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:205955			Serial	9140
Permanent link to this record



	Author	Yao, W.; Niinemets, Ü.; Yao, W.; Gielis, J.; Schrader, J.; Yu, K.; Shi, P.
	Title	Comparison of two simplified versions of the Gielis equation for describing the shape of bamboo leaves			Type	A1 Journal article
	Year	2022	Publication	Plants	Abbreviated Journal
	Volume	11	Issue	22	Pages	3058-11
	Keywords	A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Bamboo is an important component in subtropical and tropical forest communities. The plant has characteristic long lanceolate leaves with parallel venation. Prior studies have shown that the leaf shapes of this plant group can be well described by a simplified version (referred to as SGE-1) of the Gielis equation, a polar coordinate equation extended from the superellipse equation. SGE-1 with only two model parameters is less complex than the original Gielis equation with six parameters. Previous studies have seldom tested whether other simplified versions of the Gielis equation are superior to SGE-1 in fitting empirical leaf shape data. In the present study, we compared a three-parameter Gielis equation (referred to as SGE-2) with the two-parameter SGE-1 using the leaf boundary coordinate data of six bamboo species within the same genus that have representative long lanceolate leaves, with >300 leaves for each species. We sampled 2000 data points at approximately equidistant locations on the boundary of each leaf, and estimated the parameters for the two models. The root–mean–square error (RMSE) between the observed and predicted radii from the polar point to data points on the boundary of each leaf was used as a measure of the model goodness of fit, and the mean percent error between the RMSEs from fitting SGE-1 and SGE-2 was used to examine whether the introduction of an additional parameter in SGE-1 remarkably improves the model’s fitting. We found that the RMSE value of SGE-2 was always smaller than that of SGE-1. The mean percent errors among the two models ranged from 7.5% to 20% across the six species. These results indicate that SGE-2 is superior to SGE-1 and should be used in fitting leaf shapes. We argue that the results of the current study can be potentially extended to other lanceolate leaf shapes.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos	000887783400001	Publication Date	2022-11-14
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	2223-7747	ISBN		Additional Links	UA library record; WoS full record; WoS citing articles
	Impact Factor		Times cited		Open Access	OpenAccess
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:191859			Serial	7289
Permanent link to this record



	Author	Gielis, J.
	Title	Conquering Mount Improbable			Type	P1 Proceeding
	Year	2023	Publication		Abbreviated Journal
	Volume		Issue		Pages	153-173 T2 - Proceedings of the 1st International
	Keywords	P1 Proceeding; Economics; Sustainable Energy, Air and Water Technology (DuEL)
	Abstract	Our scientific and technological worldviews are largely dominated by the concepts of entropy and complexity. Originating in 19th-century thermodynamics, the concept of entropy merged with information in the last century, leading to definitions of entropy and complexity by Kolmogorov, Shannon and others. In its simplest form, this worldview is an application of the normal rules of arithmetic. In this worldview, when tossing a coin, a million heads or tails in a row is theoretically possible, but impossible in practice and in real life. On this basis, the impossible (in the binary case, the outermost entries of Pascal's triangle xn and yn for large values of n) can be safely neglected, and one can concentrate fully on what is common and what conforms to the law of large numbers, in fields ranging from physics to sociology and everything in between. However, in recent decades it has been shown that what is most improbable tends to be the rule in nature. Indeed, if one combines the outermost entries xn and yn with the normal rules of arithmetic, either addition or multiplication, one obtains Lamé curves and power laws respectively. In this article, some of these correspondences are highlighted, leading to a double conclusion. First, Gabriel Lamé's geometric footprint in mathematics and the sciences is enormous. Second, conic sections are at the core once more. Whereas mathematics so far has been exclusively the language of patterns in the sciences, the door is opened for mathematics to also become the language of the individual. The probabilistic worldview and Lamé's footprint can be seen as dual methods. In this context, it is to be expected that the notions of information, complexity, simplicity and redundancy benefit from this different viewpoint.
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date	2023-11-29
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN	978-90-833839-0-3	ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	Most recent IF: NA
	Call Number	UA @ admin @ c:irua:201045			Serial	9014
Permanent link to this record



	Author	Van den Akker, S.; Bormans, P.; Peeters, H.; Gielis, J.; Prinsen, E.
	Title	Cytokinin dynamics in cell suspension cultures of Bambusa balcooa Roxburgh using UPLC-ESI/MS/MS			Type	H3 Book chapter
	Year	2012	Publication		Abbreviated Journal
	Volume		Issue		Pages	539-547 T2 - Proceedings of the 9th World Bamboo C
	Keywords	H3 Book chapter; Engineering sciences. Technology; Integrated Molecular Plant Physiology Research (IMPRES); Sustainable Energy, Air and Water Technology (DuEL)
	Abstract
	Address
	Corporate Author				Thesis
	Publisher		Place of Publication		Editor
	Language		Wos		Publication Date
	Series Editor		Series Title		Abbreviated Series Title
	Series Volume		Series Issue		Edition
	ISSN		ISBN		Additional Links	UA library record
	Impact Factor		Times cited		Open Access
	Notes				Approved	no
	Call Number	UA @ admin @ c:irua:97754			Serial	7750
Permanent link to this record