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Records |
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Author |
Shi, P.; Wang, L.; Quinn, B.K.K.; Gielis, J. |
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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 |
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Year |
2023 |
Publication |
Symmetry |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
15 |
Issue |
1 |
Pages |
231-10 |
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Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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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. |
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Wos |
000927531000001 |
Publication Date |
2023-01-13 |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2073-8994 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
2.7 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 2.7; 2023 IF: 1.457 |
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Call Number |
UA @ admin @ c:irua:195347 |
Serial |
7279 |
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Permanent link to this record |
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Author |
Yao, W.; Niinemets, Ü.; Yao, W.; Gielis, J.; Schrader, J.; Yu, K.; Shi, P. |
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Title |
Comparison of two simplified versions of the Gielis equation for describing the shape of bamboo leaves |
Type |
A1 Journal article |
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Year |
2022 |
Publication |
Plants |
Abbreviated Journal |
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Volume |
11 |
Issue |
22 |
Pages |
3058-11 |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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. |
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Wos |
000887783400001 |
Publication Date |
2022-11-14 |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2223-7747 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
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Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:191859 |
Serial |
7289 |
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Permanent link to this record |
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Author |
Wang, L.; Ratkowsky, D.A.; Gielis, J.; Ricci, P.E.; Shi, P. |
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Title |
Effects of the numerical values of the parameters in the Gielis equation on its geometries |
Type |
A1 Journal article |
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Year |
2022 |
Publication |
Symmetry |
Abbreviated Journal |
Symmetry-Basel |
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Volume |
14 |
Issue |
12 |
Pages |
2475-12 |
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Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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Abstract |
The Lamé curve is an extension of an ellipse, the latter being a special case. Dr. Johan Gielis further extended the Lamé curve in the polar coordinate system by introducing additional parameters (n1, n2, n3; m): rφ=1Acosm4φn2+1Bsinm4φn3−1/n1, which can be applied to model natural geometries. Here, r is the polar radius corresponding to the polar angle φ; A, B, n1, n2 and n3 are parameters to be estimated; m is the positive real number that determines the number of angles of the Gielis curve. Most prior studies on the Gielis equation focused mainly on its applications. However, the Gielis equation can also generate a large number of shapes that are rotationally symmetric and axisymmetric when A = B and n2 = n3, interrelated with the parameter m, with the parameters n1 and n2 determining the shapes of the curves. In this paper, we prove the relationship between m and the rotational symmetry and axial symmetry of the Gielis curve from a theoretical point of view with the condition A = B, n2 = n3. We also set n1 and n2 to take negative real numbers rather than only taking positive real numbers, then classify the curves based on extremal properties of r(φ) at φ = 0, π/m when n1 and n2 are in different intervals, and analyze how n1, n2 precisely affect the shapes of Gielis curves. |
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Wos |
000904525700001 |
Publication Date |
2022-11-23 |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
2073-8994 |
ISBN |
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Additional Links |
UA library record; WoS full record |
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Impact Factor |
2.7 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 2.7 |
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Call Number |
UA @ admin @ c:irua:191860 |
Serial |
7301 |
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Permanent link to this record |
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Author |
Shi, P.; Yu, K.; Niinemets, Ü.; Gielis, J. |
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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 |
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Year |
2021 |
Publication |
Forests |
Abbreviated Journal |
Forests |
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Volume |
12 |
Issue |
1 |
Pages |
41 |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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. |
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Wos |
000611074700001 |
Publication Date |
2020-12-31 |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1999-4907 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
1.951 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 1.951 |
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Call Number |
UA @ admin @ c:irua:174473 |
Serial |
7572 |
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Permanent link to this record |
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Author |
Niklas, K.J.; Shi, P.; Gielis, J.; Schrader, J.; Niinemets, U. |
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Title |
Editorial: leaf functional traits : ecological and evolutionary implications |
Type |
Editorial |
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Year |
2023 |
Publication |
Frontiers in plant science |
Abbreviated Journal |
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Volume |
14 |
Issue |
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Pages |
1169558-5 |
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Keywords |
Editorial; Sustainable Energy, Air and Water Technology (DuEL) |
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Wos |
000964122500001 |
Publication Date |
2023-03-21 |
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Series Editor |
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Series Title |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
1664-462x |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
5.6 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 5.6; 2023 IF: 4.298 |
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Call Number |
UA @ admin @ c:irua:196076 |
Serial |
7834 |
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Permanent link to this record |
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Author |
Gielis, J.; Ricci, P.E.; Tavkhelidze, I. |
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Title |
The Möbius phenomenon in Generalized Möbius-Listing surfaces and bodies, and Arnold's Cat phenomenon |
Type |
A1 Journal article |
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Year |
2021 |
Publication |
Advanced Studies : Euro-Tbilisi Mathematical Journal |
Abbreviated Journal |
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Volume |
14 |
Issue |
4 |
Pages |
17-35 |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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. |
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Wos |
000774655100002 |
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Additional Links |
UA library record; WoS full record |
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Impact Factor |
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Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:183081 |
Serial |
8258 |
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Permanent link to this record |
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Author |
Gielis, J. |
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Title |
Phi-bonacci in Ancient Greece |
Type |
A1 Journal article |
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Year |
2021 |
Publication |
Symmetry : culture and science |
Abbreviated Journal |
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Volume |
32 |
Issue |
1 |
Pages |
25-40 |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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. |
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Wos |
000643822700002 |
Publication Date |
2021-03-30 |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0865-4824 |
ISBN |
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Additional Links |
UA library record; WoS full record |
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Impact Factor |
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Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:178322 |
Serial |
8376 |
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Permanent link to this record |
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Author |
Shi, P.; Chen, L.; Quinn, B.K.; Yu, K.; Miao, Q.; Guo, X.; Lian, M.; Gielis, J.; Niklas, K.J. |
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Title |
A simple way to calculate the volume and surface area of avian eggs |
Type |
A1 Journal article |
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Year |
2023 |
Publication |
Annals of the New York Academy of Sciences |
Abbreviated Journal |
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Volume |
1524 |
Issue |
1 |
Pages |
118-131 |
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Keywords |
A1 Journal article; Engineering sciences. Technology; Sustainable Energy, Air and Water Technology (DuEL) |
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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. |
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Wos |
000975679400001 |
Publication Date |
2023-04-28 |
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Series Editor |
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Abbreviated Series Title |
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Series Volume |
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Series Issue |
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Edition |
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ISSN |
0077-8923; 1749-6632 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
5.2 |
Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: 5.2; 2023 IF: 4.706 |
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Call Number |
UA @ admin @ c:irua:196724 |
Serial |
8827 |
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Permanent link to this record |
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Author |
Gielis, J. |
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Title |
Fred Van Oystaeyen : Time hybrids: a new generic theory of reality |
Type |
Review |
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Year |
2023 |
Publication |
Symmetry, Culture and Science |
Abbreviated Journal |
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Volume |
34 |
Issue |
3 |
Pages |
347-351 |
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Keywords |
Review; Sustainable Energy, Air and Water Technology (DuEL) |
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Additional Links |
UA library record |
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Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:199538 |
Serial |
8871 |
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Permanent link to this record |
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Author |
Huang, L.; Ratkowsky, D.A.; Hui, C.; Gielis, J.; Lian, M.; Shi, P. |
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Title |
Inequality measure of leaf area distribution for a drought-tolerant landscape plant |
Type |
A1 Journal article |
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Year |
2023 |
Publication |
Plants |
Abbreviated Journal |
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Volume |
12 |
Issue |
17 |
Pages |
3143-11 |
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Keywords |
A1 Journal article; Sustainable Energy, Air and Water Technology (DuEL) |
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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. |
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Wos |
001065193100001 |
Publication Date |
2023-08-31 |
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Edition |
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ISSN |
2223-7747 |
ISBN |
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Additional Links |
UA library record; WoS full record; WoS citing articles |
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Impact Factor |
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Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:199564 |
Serial |
8886 |
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Permanent link to this record |
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Author |
Shi, P.; Gielis, J.; Niklas, K.J.; Niinemets, Ü.; Schrader, J. |
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Title |
Leaf functional traits : ecological and evolutionary implications |
Type |
ME3 Book as editor |
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Year |
2023 |
Publication |
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Abbreviated Journal |
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Volume |
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Issue |
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Pages |
185 p. |
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Keywords |
ME3 Book as editor; Sustainable Energy, Air and Water Technology (DuEL) |
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Publication Date |
2023-04-14 |
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ISBN |
978-2-8325-2086-4; 1664-8714 |
Additional Links |
UA library record |
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Impact Factor |
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Times cited |
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Open Access |
OpenAccess |
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Notes |
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Approved |
Most recent IF: NA |
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Call Number |
UA @ admin @ c:irua:198002 |
Serial |
8894 |
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Permanent link to this record |