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A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Algorithms and Mathematical Models for Computer-Assisted Diagnostic Systems".

Deadline for manuscript submissions: 30 September 2024 | Viewed by 1882

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Prof. Dr. Alicia Cordero

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Guest Editor

School of Telecommunications Engineering, Universitat Politècnica de València, 46022 Valencia, Spain
Interests: numerical analysis; iterative methods; nonlinear problems; discrete dynamics, real and complex
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Prof. Dr. Juan Ramón Torregrosa Sánchez

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Institute for Multidisciplinary Mathematics, Universitat Politècnica de València, 46022 València, Spain
Interests: iterative processes; matrix analysis; numerical analysis
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Special Issue Information

Dear Colleagues,

The objective of this Special Issue, “Mathematical Modelling in Engineering and Human Behaviour 2024” (in collaboration with Mathematical Modelling in Engineering & Human Behaviour 2024—MME&HB2024, https://imm.webs.upv.es/jornadas/2024/home.html), is to develop an interdisciplinary forum in areas like Medicine, Sociology, Business and Engineering, where the latest mathematical techniques can be discussed in a common and understandable language with experts in cross-disciplinary areas. The conference is aimed at gathering researchers who need mathematics for the formulation and analysis of models.

The main topics of the conference are:

Mathematical models in epidemiology and medicine.
Mathematical models in engineering.
Applications of linear algebra.
Iterative methods for nonlinear problems.
Simulations in civil engineering and railway engineering.
Networks and applications.
Financial mathematics.
Uncertainty quantification and modelling.
Optimization, least squares and applications.
Machine learning and neuronal networks.
Mathematics for decision-making.

Prof. Dr. Alicia Cordero
Prof. Dr. Juan Ramón Torregrosa Sánchez
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at mdpi.longhoe.net 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. Algorithms 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 1600 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

mathematical models in epidemiology and medicine
mathematical models in engineering
applications of linear algebra
iterative methods for nonlinear problems
simulations in civil engineering and railway engineering
networks and applications
financial mathematics
uncertainty quantification and modelling
optimization, least squares and applications
machine learning and neuronal networks
mathematics for decision making

Related Special Issue

Mathematical Modelling in Engineering and Human Behaviour in Algorithms (8 articles)

Published Papers (4 papers)

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Research

34 pages, 628 KiB

Open AccessArticle

Fuzzy Fractional Brownian Motion: Review and Extension

by Georgy Urumov, Panagiotis Chountas and Thierry Chaussalet

Algorithms 2024, 17(7), 289; https://doi.org/10.3390/a17070289 - 1 Jul 2024

Viewed by 207

Abstract

In traditional finance, option prices are typically calculated using crisp sets of variables. However, as reported in the literature novel, these parameters possess a degree of fuzziness or uncertainty. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. This paper presents a comprehensive review of existing work on fuzzy fractional Brownian motion and proposes an extension in the context of financial option pricing. In this paper, we define a unified framework combining fractional Brownian motion with fuzzy processes, creating a joint product measure space that captures both randomness and fuzziness. The approach allows for the consideration of individual risk preferences and beliefs about parameter uncertainties. By extending Merton’s jump-diffusion model to include fuzzy fractional Brownian motion, this paper addresses the modelling needs of hybrid systems with uncertain variables. The proposed model, which includes fuzzy Poisson processes and fuzzy volatility, demonstrates advantageous properties such as long-range dependence and self-similarity, providing a robust tool for modelling financial markets. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (2nd Edition))

25 pages, 1790 KiB

Open AccessArticle

A Non-Gradient and Non-Iterative Method for Map** 3D Mesh Objects Based on a Summation of Dependent Random Values

by Ihar Volkau, Sergei Krasovskii, Abdul Mujeeb and Helen Balinsky

Algorithms 2024, 17(6), 248; https://doi.org/10.3390/a17060248 - 6 Jun 2024

Viewed by 411

Abstract

The manuscript presents a novel non-gradient and non-iterative method for map** two 3D objects by matching extrema. This innovative approach utilizes the amplification of extrema through the summation of dependent random values, accompanied by a comprehensive explanation of the statistical background. The method further incorporates structural patterns based on spherical harmonic functions to calculate the rotation matrix, enabling the juxtaposition of the objects. Without utilizing gradients and iterations to improve the solution step by step, the proposed method generates a limited number of candidates, and the map** (if it exists) is necessarily among the candidates. For instance, this method holds potential for object analysis and identification in additive manufacturing for 3D printing and protein matching. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (2nd Edition))

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18 pages, 3005 KiB

Open AccessArticle

A Modified Analytic Hierarchy Process Suitable for Online Survey Preference Elicitation

by Sean Pascoe, Anna Farmery, Rachel Nichols, Sarah Lothian and Kamal Azmi

Algorithms 2024, 17(6), 245; https://doi.org/10.3390/a17060245 - 6 Jun 2024

Viewed by 351

Abstract

A key component of multi-criteria decision analysis is the estimation of criteria weights, reflecting the preference strength of different stakeholder groups related to different objectives. One common method is the Analytic Hierarchy Process (AHP). A key challenge with the AHP is the potential for inconsistency in responses, resulting in potentially unreliable preference weights. In small groups, interactions between analysts and respondents can compensate for this through reassessment of inconsistent responses. In many cases, however, stakeholders may be geographically dispersed, with online surveys being a more cost-effective means to elicit these preferences, making renegotiating with inconsistent respondents impossible. Further, the potentially large number of bivariate comparisons required using the AHP may adversely affect response rates. In this study, we test a new “modified” AHP (MAHP). The MAHP was designed to retain the key desirable features of the AHP but be more amenable to online surveys, reduce the problem of inconsistencies, and require substantially fewer comparisons. The MAHP is tested using three groups of university students through an online survey platform, along with a “traditional” AHP approach. The results indicate that the MAHP can provide statistically equivalent outcomes to the AHP but without problems arising due to inconsistencies. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (2nd Edition))

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11 pages, 272 KiB

Open AccessArticle

Three Cube Packing for All Dimensions

by Peter Adamko

Algorithms 2024, 17(5), 198; https://doi.org/10.3390/a17050198 - 8 May 2024

Viewed by 615

Abstract

Let

V_{n} (d)

denote the least number, such that every collection of n d-cubes with total volume 1 in d-dimensional (Euclidean) space can be packed parallelly into some d-box of volume

V_{n} (d)

[...] Read more.

Let

V_{n} (d)

denote the least number, such that every collection of n d-cubes with total volume 1 in d-dimensional (Euclidean) space can be packed parallelly into some d-box of volume

V_{n} (d)

. We show that

V_{3} (d) = \frac{r^{1 - d}}{d}

d \geq 11

and

V_{3} (d) = \frac{\frac{1}{r} + 1}{r^{d} + {(\frac{1}{r} - r)}^{d} + 1}

2 \leq d \leq 10

, where r is the only solution of the equation

2 (d - 1) k^{d} + d k^{d - 1} = 1

(\frac{\sqrt{2}}{2}, 1)

and

{(k + 1)}^{d} {(1 - k)}^{d - 1} (d k^{2} + d + k - 1) = k^{d} (d k^{d + 1} + d k^{d} + k^{d} + 1)

(\frac{\sqrt{2}}{2}, 1)

, respectively. The maximum volume is achieved by hypercubes with edges x, y, z, such that

x = {(2 r^{d} + 1)}^{- 1 / d}

y = z = r x

d \geq 11

, and

x = {(r^{d} + {(\frac{1}{r} - r)}^{d} + 1)}^{- 1 / d}

y = r x

z = (\frac{1}{r} - r) x

2 \leq d \leq 10

. We also proved that only for dimensions less than 11 are there two different maximum packings, and for all dimensions greater than 10, the maximum packing has the same two smallest cubes. Full article

(This article belongs to the Special Issue Mathematical Modelling in Engineering and Human Behaviour (2nd Edition))

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