Algorithms

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13 pages, 696 KiB

Open AccessArticle

PIPET: A Pipeline to Generate PET Phantom Datasets for Reconstruction Based on Convolutional Neural Network Training

by Alejandro Sanz-Sanchez, Francisco B. García, Pablo Mesas-Lafarga, Joan Prats-Climent and María José Rodríguez-Álvarez

Algorithms 2024, 17(11), 511; https://doi.org/10.3390/a17110511 - 7 Nov 2024

Viewed by 621

Abstract

There has been a strong interest in using neural networks to solve several tasks in PET medical imaging. One of the main problems faced when using neural networks is the quality, quantity, and availability of data to train the algorithms. In order to [...] Read more.

There has been a strong interest in using neural networks to solve several tasks in PET medical imaging. One of the main problems faced when using neural networks is the quality, quantity, and availability of data to train the algorithms. In order to address this issue, we have developed a pipeline that enables the generation of voxelized synthetic PET phantoms, simulates the acquisition of a PET scan, and reconstructs the image from the simulated data. In order to achieve these results, several pieces of software are used in the different steps of the pipeline. This pipeline solves the problem of generating diverse PET datasets and images of high quality for different types of phantoms and configurations. The data obtained from this pipeline can be used to train convolutional neural networks for PET reconstruction. Full article

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

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16 pages, 429 KiB

Open AccessArticle

Local Convergence Study for an Iterative Scheme with a High Order of Convergence

by Eulalia Martínez and Arleen Ledesma

Algorithms 2024, 17(11), 481; https://doi.org/10.3390/a17110481 - 25 Oct 2024

Viewed by 570

Abstract

In this paper, we address a key issue in Numerical Functional Analysis: to perform the local convergence analysis of a fourth order of convergence iterative method in Banach spaces, examining conditions on the operator and its derivatives near the solution to ensure convergence. [...] Read more.

In this paper, we address a key issue in Numerical Functional Analysis: to perform the local convergence analysis of a fourth order of convergence iterative method in Banach spaces, examining conditions on the operator and its derivatives near the solution to ensure convergence. Moreover, this approach provides a local convergence ball, within which initial estimates lead to guaranteed convergence with details about the radii of domain of convergence and estimates on error bounds. Next, we perform a comparative study of the Computational Efficiency Index (

C E I

) between the analyzed scheme and some known iterative methods of fourth order of convergence. Our ultimate goal is to use these theoretical findings to address practical problems in engineering and technology. Full article

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

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33 pages, 8616 KiB

Open AccessArticle

Theoretical Study of the Wear of a Reduced-Diameter Wheel for Freight Wagons, Based on Its Diameter

by David S. Pellicer and Emilio Larrodé

Algorithms 2024, 17(10), 437; https://doi.org/10.3390/a17100437 - 1 Oct 2024

Viewed by 788

Abstract

This paper presents the development of a numerical analysis model designed to estimate the lifespan of reduced-diameter wheels used in freight wagons based on their diameter, under quasi-static conditions. These wheels are increasingly being used in combined transport applications, where they are installed [...] Read more.

This paper presents the development of a numerical analysis model designed to estimate the lifespan of reduced-diameter wheels used in freight wagons based on their diameter, under quasi-static conditions. These wheels are increasingly being used in combined transport applications, where they are installed in various bogie configurations and subjected to different operational environments. However, due to the unique characteristics of reduced-diameter wheels, their lifespan has been scarcely studied. To accurately build this model, an in-depth investigation of the rolling phenomenon was required, addressing key issues in the track–vehicle interaction and establishing relationships between these factors. After constructing the rail–wheel interaction model, it was applied to calculate the lifespan of wheels with standard, medium, and reduced diameters under identical conditions for comparison. This approach makes it possible to determine the lifespan of reduced-diameter wheels relative to standard ones, as well as to observe how lifespan changes with wheel diameter, and it is observed how lifespan diminishes non-linearly with decreasing diameters. The underlying reasons for this variation are explained through a comprehensive understanding of the rolling phenomenon, enabled by the full analysis. Full article

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

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16 pages, 522 KiB

Open AccessArticle

Numerical Algorithms for Identification of Convection Coefficient and Source in a Magnetohydrodynamics Flow

by Juri D. Kandilarov and Lubin G. Vulkov

Algorithms 2024, 17(9), 387; https://doi.org/10.3390/a17090387 - 2 Sep 2024

Viewed by 750

Abstract

We consider three integral observations inverse problems (IP1, IP2, IP3) for reconstruction of a time-dependent convection coefficient and a source in magnetohydrodynamics (MHD) model. On the first stage, using the integral observations, we reduce the inverse problems to nonclassical direct (forward) ones. The [...] Read more.

We consider three integral observations inverse problems (IP1, IP2, IP3) for reconstruction of a time-dependent convection coefficient and a source in magnetohydrodynamics (MHD) model. On the first stage, using the integral observations, we reduce the inverse problems to nonclassical direct (forward) ones. The equivalence between the inverse and direct problems is established. Then, the well-posedness of nonclassical problems is proved. Further, to overcome the difficulties arising from the nonlinear nonlocal parabolic operators, we construct a linarization algorithm in time after their difference space discretizatons. Next, on each iteration, to solve the corresponding linear systems of algebraic equations, we propose adequate fast elimination algorithms. Computational results of test examples data are discussed. Full article

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

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34 pages, 709 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 975

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, [...] Read more.

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 Mapping 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 1093

Abstract

The manuscript presents a novel non-gradient and non-iterative method for mapping 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 [...] Read more.

The manuscript presents a novel non-gradient and non-iterative method for mapping 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 mapping (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

Cited by 1 | Viewed by 944

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 [...] Read more.

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 1014

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}

if

d \geq 11

and

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

if

2 \leq d \leq 10

, where r is the only solution of the equation

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

on

(\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)

on

(\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

if

d \geq 11

, and

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

,

y = r x

,

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

if

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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