Symmetry in Mathematical Models

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: 31 October 2024 | Viewed by 496

Special Issue Editors


E-Mail Website
Guest Editor
Vinča Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, Belgrade, Serbia
Interests: machine learning; deep learning; CNN; LSTM; remote sensing data; mathematical modelling

E-Mail Website
Guest Editor
Department of Theoretical Physics and Condensed Matter Physics (020), Vinča Institute of Nuclear Sciences - National Institute of the Republic of Serbia, University of Belgrade, P.O. Box 522, 11001 Belgrade, Serbia
Interests: radioastronomy; mass spectra of elementary particles; numerical experiments; big data; gravitation and the structure of the Universe

Special Issue Information

Dear Colleagues,

Symmetry represents agreement in dimensions due to proportionality and refers to a sense of harmonious proportionality and balance. In mathematics, symmetry has a precise definition, that an object is invariant to any of a variety of transformations, including reflection, rotation, or scaling. In geometry, symmetry is the mirroring (mapping) of figures. Symmetry is the property of a symmetrical figure in relation to a line (axis), point (center) or plane. Integers are said to be symmetric (palindromes) if they are read the same on both the left and right sides. Biosymmetry studies the symmetry of biostructures at the molecular and supramolecular level and allows the determination, in advance, of the possible variants of symmetry in biological objects, strictly describing the external form and internal structure of any organism. Only two main types of symmetry are known: rotational and translational, or there is a modification from the combination of these two basic types of symmetry rotational–translational symmetry.

Therefore, the aim of this Special Issue is to showcase a range of proposed multidisciplinary studies on symmetry. Here, we want to point out that the proper mathematical model can explain it, and this Special Issue will be a collection of a number of such examples.

Dr. Dušan Nikezić
Prof. Dr. Vesna Borka Jovanović
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • artificial intelligence
  • machine learning
  • neural network
  • data analysis
  • big data in astrophysics
  • nonlinear dynamics
  • biomathematics
  • mathematical modelling
  • chaos
  • symmetry

Published Papers (1 paper)

Order results
Result details
Select all
Export citation of selected articles as:

Research

9 pages, 892 KiB  
Article
Symmetric U-Net Model Tuned by FOX Metaheuristic Algorithm for Global Prediction of High Aerosol Concentrations
by Dušan P. Nikezić, Dušan S. Radivojević, Nikola S. Mirkov, Ivan M. Lazović and Tatjana A. Miljojčić
Symmetry 2024, 16(5), 525; https://doi.org/10.3390/sym16050525 - 26 Apr 2024
Viewed by 206
Abstract
In this study, the idea of using a fully symmetric U-Net deep learning model for forecasting a segmented image of high global aerosol concentrations is implemented. As the forecast relies on historical data, the model used a sequence of the last eight segmented [...] Read more.
In this study, the idea of using a fully symmetric U-Net deep learning model for forecasting a segmented image of high global aerosol concentrations is implemented. As the forecast relies on historical data, the model used a sequence of the last eight segmented images to make the prediction. For this, the classic U-Net model was modified to use ConvLSTM2D layers with MaxPooling3D and UpSampling3D layers. In order to achieve complete symmetry, the output data are given in the form of a series of eight segmented images shifted by one image in the time sequence so that the last image actually represents the forecast of the next image of high aerosol concentrations. The proposed model structure was tuned by the new FOX metaheuristic algorithm. Based on our analysis, we found that this algorithm is suitable for tuning deep learning models considering their stochastic nature. It was also found that this algorithm spends the most time in areas close to the optimal value where there is a weaker linear correlation with the required metric and vice versa. Taking into account the characteristics of the used database, we concluded that the model is capable of generating adequate data and finding patterns in the time domain based on the ddc and dtc criteria. By comparing the achieved results of this model using the AUC-PR metric with the previous results of the ResNet3D-101 model with transfer learning, we concluded that the proposed symmetric U-Net model generates data better and is more capable of finding patterns in the time domain. Full article
(This article belongs to the Special Issue Symmetry in Mathematical Models)
Show Figures

Figure 1

Back to TopTop