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AppliedMath
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Feature Papers in AppliedMath
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Feature Papers in AppliedMath

A special issue of AppliedMath (ISSN 2673-9909).

Deadline for manuscript submissions: closed (30 December 2022) | Viewed by 22412

Special Issue Editor

Prof. Dr. Takayuki Hibi

E-Mail Website
Guest Editor
Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, 1-5 Yamadaoka, Suita 565-0871, Japan
Interests: computational commutative algebra; discrete mathematics; combinatorics
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

As Editor-in-Chief of AppliedMath, I am pleased to announce the Special Issue "Feature Papers in AppliedMath", which will be a collection of high-quality papers (original research articles or comprehensive reviews) from top academics addressing the interdisciplinary nature of Applied Mathematics. I welcome the submission of manuscripts from Editorial Board Members, and from outstanding scholars invited by the Editorial Board and the Editorial Office, related to any of the topics covered in the scope of the journal: https://www.mdpi.com/journal/appliedmath.

You are invited to send short proposals for submissions to our Editorial Office ([email protected]) for evaluation. Please note that selected full papers will still be subject to a thorough and rigorous peer-review.

Prof. Dr. Takayuki Hibi
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. AppliedMath is an international peer-reviewed open access quarterly 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 1000 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.

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Further information on MDPI's Special Issue polices can be found here.

Published Papers (7 papers)

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Research

11 pages, 283 KiB  
Article
A Sequence of Cohen–Macaulay Standard Graded Domains Whose h-Vectors Have Exponentially Deep Flaws
by Mitsuhiro Miyazaki
AppliedMath 2023, 3(2), 305-315; https://doi.org/10.3390/appliedmath3020017 - 3 Apr 2023
Viewed by 1175
Abstract
Let K be a field. In this paper, we construct a sequence of Cohen–Macaulay standard graded K-domains whose h-vectors are non-flawless and have exponentially deep flaws. Full article
(This article belongs to the Special Issue Feature Papers in AppliedMath)
21 pages, 16180 KiB  
Article
Linear Trees, Lattice Walks, and RNA Arrays
by Jasmine Renee Evans and Asamoah Nkwanta
AppliedMath 2023, 3(1), 200-220; https://doi.org/10.3390/appliedmath3010012 - 9 Mar 2023
Viewed by 2213
Abstract
The leftmost column entries of RNA arrays I and II count the RNA numbers that are related to RNA secondary structures from molecular biology. RNA secondary structures sometimes have mutations and wobble pairs. Mutations are random changes that occur in a structure, and [...] Read more.
The leftmost column entries of RNA arrays I and II count the RNA numbers that are related to RNA secondary structures from molecular biology. RNA secondary structures sometimes have mutations and wobble pairs. Mutations are random changes that occur in a structure, and wobble pairs are known as non-Watson–Crick base pairs. We used topics from RNA combinatorics and Riordan array theory to establish connections among combinatorial objects related to linear trees, lattice walks, and RNA arrays. In this paper, we establish interesting new explicit bijections (one-to-one correspondences) involving certain subclasses of linear trees, lattice walks, and RNA secondary structures. We provide an interesting generalized lattice walk interpretation of RNA array I. In addition, we provide a combinatorial interpretation of RNA array II as RNA secondary structures with n bases and k base-point mutations where ω of the structures contain wobble base pairs. We also establish an explicit bijection between RNA structures with mutations and wobble bases and a certain subclass of lattice walks. Full article
(This article belongs to the Special Issue Feature Papers in AppliedMath)
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25 pages, 13106 KiB  
Article
Analyzing Health Data Breaches: A Visual Analytics Approach
by Wullianallur Raghupathi, Viju Raghupathi and Aditya Saharia
AppliedMath 2023, 3(1), 175-199; https://doi.org/10.3390/appliedmath3010011 - 9 Mar 2023
Cited by 13 | Viewed by 8710
Abstract
This research studies the occurrence of data breaches in healthcare provider settings regarding patient data. Using visual analytics and data visualization tools, we study the distribution of healthcare breaches by state. We review the main causes and types of breaches, as well as [...] Read more.
This research studies the occurrence of data breaches in healthcare provider settings regarding patient data. Using visual analytics and data visualization tools, we study the distribution of healthcare breaches by state. We review the main causes and types of breaches, as well as their impact on both providers and patients. The research shows a range of data breach victims. Network servers are the most popular location for common breaches, such as hacking and information technology (IT) incidents, unauthorized access, theft, loss, and improper disposal. We offer proactive recommendations to prepare for a breach. These include, but are not limited to, regulatory compliance, implementing policies and procedures, and monitoring network servers. Unfortunately, the results indicate that the probability of data breaches will continue to rise. Full article
(This article belongs to the Special Issue Feature Papers in AppliedMath)
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27 pages, 468 KiB  
Article
Game of Life-like Opinion Dynamics: Generalizing the Underpopulation Rule
by Miriam Di Ianni
AppliedMath 2023, 3(1), 10-36; https://doi.org/10.3390/appliedmath3010002 - 28 Dec 2022
Cited by 1 | Viewed by 1680
Abstract
Graph dynamics for a node-labeled graph is a set of updating rules describing how the labels of each node in the graph change in time as a function of the global set of labels. The underpopulation rule is graph dynamics derived by simplifying [...] Read more.
Graph dynamics for a node-labeled graph is a set of updating rules describing how the labels of each node in the graph change in time as a function of the global set of labels. The underpopulation rule is graph dynamics derived by simplifying the set of rules constituting the Game of Life. It is known that the number of label configurations met by a graph during the dynamic process defined by such rule is bounded by a polynomial in the size of the graph if the graph is undirected. As a consequence, predicting the labels evolution is an easy problem (i.e., a problem in P) in such a case. In this paper, the generalization of the underpopulation rule to signed and directed graphs is studied. It is here proved that the number of label configurations met by a graph during the dynamic process defined by any so generalized underpopulation rule is still bounded by a polynomial in the size of the graph if the graph is undirected and structurally balanced, while it is not bounded by any polynomial in the size of the graph if the graph is directed although unsigned unless P = PSpace. Full article
(This article belongs to the Special Issue Feature Papers in AppliedMath)
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13 pages, 300 KiB  
Article
A Note on the Appearance of the Simplest Antilinear ODE in Several Physical Contexts
by Dmitry Ponomarev
AppliedMath 2022, 2(3), 433-445; https://doi.org/10.3390/appliedmath2030024 - 19 Jul 2022
Viewed by 1517
Abstract
We review several one-dimensional problems such as those involving linear Schrödinger equation, variable-coefficient Helmholtz equation, Zakharov–Shabat system and Kubelka–Munk equations. We show that they all can be reduced to solving one simple antilinear ordinary differential equation [...] Read more.
We review several one-dimensional problems such as those involving linear Schrödinger equation, variable-coefficient Helmholtz equation, Zakharov–Shabat system and Kubelka–Munk equations. We show that they all can be reduced to solving one simple antilinear ordinary differential equation u′x=fxux¯ or its nonhomogeneous version u′x=fxux¯+gx, x∈0,x0⊂R. We point out some of the advantages of the proposed reformulation and call for further investigation of the obtained ODE. Full article
(This article belongs to the Special Issue Feature Papers in AppliedMath)
16 pages, 868 KiB  
Article
One-Dimensional Matter Waves as a Multi-State Bit
by Jacopo Giacomelli
AppliedMath 2022, 2(1), 143-158; https://doi.org/10.3390/appliedmath2010008 - 1 Mar 2022
Viewed by 2418
Abstract
We design a simple technique to control the position of a localized matter wave. Our system is composed of two counter-phased periodic potentials and a third optical lattice, which can be either periodic or disordered. The only control needed on the system is [...] Read more.
We design a simple technique to control the position of a localized matter wave. Our system is composed of two counter-phased periodic potentials and a third optical lattice, which can be either periodic or disordered. The only control needed on the system is a three-state switch that allows the sudden selection of the desired potential. The method is proposed as a possible new alternative to achieving the realization of a multi-state bit. We show that this framework is robust, and that the multi-state bit behavior can be observed under weak assumptions. Given the current degree of development of matter wave control in optical lattices, we believe that the proposed device would be easily reproducible in a laboratory, allowing for testing and industrial applications. Full article
(This article belongs to the Special Issue Feature Papers in AppliedMath)
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15 pages, 13314 KiB  
Article
Non-Linear Analysis of River System Dynamics Using Recurrence Quantification Analysis
by Athanasios Fragkou, Avraam Charakopoulos, Theodoros Karakasidis and Antonios Liakopoulos
AppliedMath 2022, 2(1), 1-15; https://doi.org/10.3390/appliedmath2010001 - 6 Jan 2022
Cited by 3 | Viewed by 3393
Abstract
Understanding the underlying processes and extracting detailed characteristics of rivers is critical and has not yet been fully developed. The purpose of this study was to examine the performance of non-linear time series methods on environmental data. Specifically, we performed an analysis of [...] Read more.
Understanding the underlying processes and extracting detailed characteristics of rivers is critical and has not yet been fully developed. The purpose of this study was to examine the performance of non-linear time series methods on environmental data. Specifically, we performed an analysis of water level measurements, extracted from sensors, located on specified stations along the Nestos River (Greece), with Recurrence Plots (RP) and Recurrence Quantification Analysis (RQA) methods. A more detailed inspection with the sliding windows (epoqs) method was applied on the Recurrence Rate, Average Diagonal Line and Trapping Time parameters, with results showing phase transitions providing useful information about the dynamics of the system. The suggested method seems to be promising for the detection of the dynamical transitions that can characterize distinct time windows of the time series and reveals information about the changes in state within the whole time series. The results will be useful for designing the energy policy investments of producers and also will be helpful for dam management assessment as well as government energy policy. Full article
(This article belongs to the Special Issue Feature Papers in AppliedMath)
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