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Mathematics
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Advances on Complex Systems with Mathematics and Computer Science
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Advances on Complex Systems with Mathematics and Computer Science

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

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 2913

Special Issue Editor

Prof. Dr. Christophe Guyeux

E-Mail Website
Guest Editor
Department of Computer Science, Femto-ST Institute, UMR 6174 CNRS, Université de Bourgogne-Franche-Comté, Dijon, France
Interests: bioinformatics; artificial intelligence; complex systems; chaos theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

A complex system is a set of many interacting entities whose integration achieves a common goal. Complex systems are characterized by emergent properties that exist only at the system level and cannot be observed at the level of its constituents. In some cases, an observer cannot predict the feedbacks or the behaviors or evolutions of complex systems by calculation, which leads to studying them using tools such as chaos theory, artificial intelligence, graph theory, or statistics.

The ambition of this Special Issue is to review the latest advances in the field of complex systems and at the interface of mathematics and computer science. Contributions can be theoretical or practical, as long as they shed new light on the complexity of such systems, or on how to deal with it.

Prof. Dr. Christophe Guyeux
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

  • complex systems
  • artificial intelligence
  • large graphs
  • bioinformatics
  • chaos theory

Published Papers (3 papers)

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Research

15 pages, 272 KiB  
Article
An Improved Coppersmith Algorithm Based on Block Preprocessing
by Lu Zhang, Baodong Qin, Wen Gao and Yiyuan Luo
Mathematics 2024, 12(2), 173; https://doi.org/10.3390/math12020173 - 05 Jan 2024
Viewed by 521
Abstract
Since Coppersmith proposed the use of the LLL algorithm to solve univariate modular polynomial equations at EUROCRYPT’96, it has sparked a fervent research interest in lattice analysis among cryptographers. Despite its polynomial-time nature, the LLL algorithm exhibits a high-order polynomial upper bound in [...] Read more.
Since Coppersmith proposed the use of the LLL algorithm to solve univariate modular polynomial equations at EUROCRYPT’96, it has sparked a fervent research interest in lattice analysis among cryptographers. Despite its polynomial-time nature, the LLL algorithm exhibits a high-order polynomial upper bound in terms of theoretical complexity, particularly with longer computation times when applied to high-dimensional lattices. In addressing this issue, we propose an improved algorithm based on block preprocessing, building on the original Coppersmith algorithm and thus providing proof of correctness for this algorithm. This approach effectively reduces the solution time of the algorithm, offering a maximum improvement of 8.1% compared to the original Coppersmith algorithm. Additionally, we demonstrate the compatibility of our algorithm with the rounding algorithm proposed at PKC 2014. The combined utilization of these approaches further enhances the efficiency of our algorithm. The experimental results show that the combined algorithm achieves a maximum improvement of 22.4% in solution time compared to the original Coppersmith algorithm. It also outperforms the standalone rounding algorithm with a maximum improvement of 12.1%. When compared to the improved Coppersmith algorithm based on row common factor extraction, our proposed algorithm demonstrates comparable or even superior performance in certain dimensions. The block preprocessing algorithm in our approach enables independent execution without data exchange, making it suitable for leveraging multi-processing advantages in scenarios involving higher degrees of modular polynomial equations. This offers a new perspective for achieving the parallel computation of the Coppersmith algorithm, facilitating parallel execution and providing valuable insights. Full article
(This article belongs to the Special Issue Advances on Complex Systems with Mathematics and Computer Science)
13 pages, 21619 KiB  
Article
Mean-Field Analysis with Random Perturbations to Detect Gliders in Cellular Automata
by Juan Carlos Seck-Tuoh-Mora, Joselito Medina-Marin, Norberto Hernández-Romero and Genaro J. Martínez
Mathematics 2023, 11(20), 4319; https://doi.org/10.3390/math11204319 - 17 Oct 2023
Viewed by 697
Abstract
Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known [...] Read more.
Cellular automata are mathematical models that represent systems with complex behavior through simple interactions between their individual elements. These models can be used to study unconventional computational systems and complexity. One notable aspect of cellular automata is their ability to create structures known as gliders, which move in a regular pattern to represent the manipulation of information. This paper introduces the modification of mean-field theory applied to cellular automata, using random perturbations based on the system’s evolution rule. The original aspect of this approach is that the perturbation factor is tailored to the nature of the rule, altering the behavior of the mean-field polynomials. By combining the properties of both the original and perturbed polynomials, it is possible to detect when a cellular automaton is more likely to generate gliders without having to run evolutions of the system. This methodology is a useful approach to finding more examples of cellular automata that exhibit complex behavior. We start by examining elementary cellular automata, then move on to examples of automata that can generate gliders with more states. To illustrate the results of this methodology, we provide evolution examples of the detected automata. Full article
(This article belongs to the Special Issue Advances on Complex Systems with Mathematics and Computer Science)
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14 pages, 593 KiB  
Article
On Targeted Control over Trajectories of Dynamical Systems Arising in Models of Complex Networks
by Diana Ogorelova, Felix Sadyrbaev and Inna Samuilik
Mathematics 2023, 11(9), 2206; https://doi.org/10.3390/math11092206 - 08 May 2023
Cited by 3 | Viewed by 1116
Abstract
The question of targeted control over trajectories of systems of differential equations encountered in the theory of genetic and neural networks is considered. Examples are given of transferring trajectories corresponding to network states from the basin of attraction of one attractor to the [...] Read more.
The question of targeted control over trajectories of systems of differential equations encountered in the theory of genetic and neural networks is considered. Examples are given of transferring trajectories corresponding to network states from the basin of attraction of one attractor to the basin of attraction of the target attractor. This article considers a system of ordinary differential equations that arises in the theory of gene networks. Each trajectory describes the current and future states of the network. The question of the possibility of reorienting a given trajectory from the initial state to the assigned attractor is considered. This implies an only partial control of the network. The difficulty lies in the selection of parameters, the change of which leads to the goal. Similar problems arise when modeling the response of the body’s gene networks to serious diseases (e.g., leukemia). Solving such problems is the first step in the process of applying mathematical methods in medicine and pharmacology. Full article
(This article belongs to the Special Issue Advances on Complex Systems with Mathematics and Computer Science)
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