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Dear Colleagues,

Symmetry 2017—The First International Conference on Symmetry (http://sciforum.net/conference/symmetry2017), organized by the MDPI journal Symmetry, will be held in Barcelona, Spain, 16–18 October 2017. We welcome scholars, engineers, students and enterprises to join this big event, and submit abstracts to our conference website.

To promote the results of abstract submissions, we will collect the conference proceedings in an electronic book format and announce this on the Symmetry webpage (https://www.mdpi.com/journal/symmetry). In addition, we have set up this Special Issue to publish full papers from the conference.

Manuscripts submitted to our journal Symmetry will receive a thorough peer review and fast publication.

Prof. Dr. Sergei D. Odintsov
Prof. Dr. Kimball A. Milton
Prof. Dr. Cino Pertoldi
Prof. Dr. Maurizio Benaglia
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18 pages, 5744 KiB

Open AccessArticle

Towards More Realistic Leaf Shapes in Functional-Structural Plant Models

by Dominik Schmidt and Katrin Kahlen

Symmetry 2018, 10(7), 278; https://doi.org/10.3390/sym10070278 - 12 Jul 2018

Cited by 13 | Viewed by 4687

Abstract

Fluctuating asymmetry in plant leaves is a widely used measure in geometric morphometrics for assessing random deviations from perfect symmetry. In this study, we considered the concept of fluctuating asymmetry to improve the prototype leaf shape of the functional-structural plant model L-Cucumber. The overall objective was to provide a realistic geometric representation of the leaves for the light sensitive plant reactions in the virtual plant model. Based on three-dimensional data from several hundred in situ digitized cucumber leaves comparisons of model leaves and measurements were conducted. Robust Bayesian comparison of groups was used to assess statistical differences between leaf halves while respecting fluctuating asymmetries. Results indicated almost no directional asymmetry in leaves comparing different distances from the prototype while detecting systematic deviations shared by both halves. This information was successfully included in an improved leaf prototype and implemented in the virtual plant model L-Cucumber. Comparative virtual plant simulations revealed a slight improvement in plant internode development against experimental data using the novel leaf shape. Further studies can now focus on analyses of stress on the 3D-deformation of the leaf and the development of a dynamic leaf shape model. Full article

(This article belongs to the Special Issue Selected Papers: Symmetry 2017—The First International Conference on Symmetry)

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13 pages, 273 KiB

Open AccessArticle

Symmetric Representation of Ternary Forms Associated to Some Toeplitz Matrices ^†

by Mao-Ting Chien and Hiroshi Nakazato

Symmetry 2018, 10(3), 55; https://doi.org/10.3390/sym10030055 - 27 Feb 2018

Viewed by 2390

Abstract

Let A be an

n \times n

complex matrix. Assume the determinantal curve [...] Read more.

Let A be an

n \times n

complex matrix. Assume the determinantal curve

V_{A} = {[(x, y, z)] \in {CP}^{2} : F_{A} (x, y, z) = \det (x ℜ (A) + y ℑ (A) + z I_{n}) = 0}

is a rational curve. The Fiedler formula provides a complex symmetric matrix S satisfying

F_{S} (x, y, z) = F_{A} (x, y, z)

. It is also known that every Toeplitz matrix is unitarily similar to a symmetric matrix. In this paper, we investigate the unitary similarity of the symmetric matrix S and the matrix A in the Fiedler theorem for a specific parametrized family of

4 \times 4

nilpotent Toeplitz matrices A. We show that there are either one or at least three unitarily inequivalent symmetric matrices which admit the determinantal representation of the ternary from

F_{A} (x, y, z)

associated to the specific

4 \times 4

nilpotent Toeplitz matrices. Full article

(This article belongs to the Special Issue Selected Papers: Symmetry 2017—The First International Conference on Symmetry)

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