Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
3.5
2.4
Journals
Mathematics
Special Issues
Group Theory and its Applications in Engineering, Computer Science, and...
share announcement

Group Theory and its Applications in Engineering, Computer Science, and Structural Biology

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (30 December 2020) | Viewed by 10564

Special Issue Editor

Prof. Dr. Simone Fiori

E-Mail Website
Guest Editor
Department of Information Engineering, Marches Polytechnic University, 60121 Ancona, Italy
Interests: computational intelligence; geometric numerical integration; numerical methods in applied sciences and engineering; differential geometrical methods in applied sciences and engineering
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

For the past century, group-theoretic methods have been a cornerstone of all aspects of physics. More recently, group theory has been applied widely outside of physics, in fields ranging from robotics and computer vision, to the study of biomolecular symmetry and conformation, to the study of how information is processed in deep learning and in the mammalian visual cortex.

This Special Issue focuses on group theory as it relates to these applications. Moreover, the development of new and efficient computational tools that use group theory with these applications in mind are welcome.

Prof. Simone Fiori
Guest Editor

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. Mathematics is an international peer-reviewed open access semimonthly 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 2600 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

  • Group theory
  • Algorithms
  • Pattern recognition
  • Robotics
  • Computer vision
  • Visual cortex
  • Crystallography
  • Molecular symmetry

Published Papers (3 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

13 pages, 309 KiB  
Article
Theoretical Bounds on Performance in Threshold Group Testing Schemes
by Jin-Taek Seong
Mathematics 2020, 8(4), 637; https://doi.org/10.3390/math8040637 - 21 Apr 2020
Cited by 4 | Viewed by 2322
Abstract
A threshold group testing (TGT) scheme with lower and upper thresholds is a general model of group testing (GT) which identifies a small set of defective samples. In this paper, we consider the TGT scheme that require the minimum number of tests. We [...] Read more.
A threshold group testing (TGT) scheme with lower and upper thresholds is a general model of group testing (GT) which identifies a small set of defective samples. In this paper, we consider the TGT scheme that require the minimum number of tests. We aim to find lower and upper bounds for finding a set of defective samples in a large population. The decoding for the TGT scheme is exploited by minimization of the Hamming weight in channel coding theory and the probability of error is also defined. Then, we derive a new upper bound on the probability of error and extend a lower bound from conventional one to the TGT scheme. We show that the upper and lower bounds well match with each other at the optimal density ratio of the group matrix. In addition, we conclude that when the gaps between the two thresholds in the TGT framework increase, the group matrix with a high density should be used to achieve optimal performance. Full article
(This article belongs to the Special Issue Group Theory and its Applications in Engineering, Computer Science, and Structural Biology)
►▼ Show Figures

Figure 1

35 pages, 2414 KiB  
Article
Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors
by Simone Fiori
Mathematics 2019, 7(10), 935; https://doi.org/10.3390/math7100935 - 10 Oct 2019
Cited by 13 | Viewed by 3367
Abstract
The present paper recalls a formulation of non-conservative system dynamics through the Lagrange–d’Alembert principle expressed through a generalized Euler–Poincaré form of the system equation on a Lie group. The paper illustrates applications of the generalized Euler–Poincaré equations on the rotation groups to a [...] Read more.
The present paper recalls a formulation of non-conservative system dynamics through the Lagrange–d’Alembert principle expressed through a generalized Euler–Poincaré form of the system equation on a Lie group. The paper illustrates applications of the generalized Euler–Poincaré equations on the rotation groups to a gyrostat satellite and a quadcopter drone. The numerical solution of the dynamical equations on the rotation groups is tackled via a generalized forward Euler method and an explicit Runge–Kutta integration method tailored to Lie groups. Full article
(This article belongs to the Special Issue Group Theory and its Applications in Engineering, Computer Science, and Structural Biology)
►▼ Show Figures

Figure 1

10 pages, 305 KiB  
Article
Some New Applications of Weakly ℋ-Embedded Subgroups of Finite Groups
by Li Zhang, Li-Jun Huo and Jia-Bao Liu
Mathematics 2019, 7(2), 158; https://doi.org/10.3390/math7020158 - 10 Feb 2019
Viewed by 2349
Abstract
A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H ∩ T ∈ H ( G ) , [...] Read more.
A subgroup H of a finite group G is said to be weakly H -embedded in G if there exists a normal subgroup T of G such that H G = H T and H ∩ T ∈ H ( G ) , where H G is the normal closure of H in G, and H ( G ) is the set of all H -subgroups of G. In the recent research, Asaad, Ramadan and Heliel gave new characterization of p-nilpotent: Let p be the smallest prime dividing | G | , and P a non-cyclic Sylow p-subgroup of G. Then G is p-nilpotent if and only if there exists a p-power d with 1 < d < | P | such that all subgroups of P of order d and p d are weakly H -embedded in G. As new applications of weakly H -embedded subgroups, in this paper, (1) we generalize this result for general prime p and get a new criterion for p-supersolubility; (2) adding the condition “ N G ( P ) is p-nilpotent”, here N G ( P ) = { g ∈ G | P g = P } is the normalizer of P in G, we obtain p-nilpotence for general prime p. Moreover, our tool is the weakly H -embedded subgroup. However, instead of the normality of H G = H T , we just need H T is S-quasinormal in G, which means that H T permutes with every Sylow subgroup of G. Full article
(This article belongs to the Special Issue Group Theory and its Applications in Engineering, Computer Science, and Structural Biology)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop