Computation

19 pages, 9366 KiB

Open AccessArticle

Computational Methods in the Drug Delivery of Carbon Nanocarriers onto Several Compounds in Sarraceniaceae Medicinal Plant as Monkeypox Therapy

by Fatemeh Mollaamin

Computation 2023, 11(4), 84; https://doi.org/10.3390/computation11040084 - 20 Apr 2023

Cited by 4 | Viewed by 1176

Abstract

In this article, monkeypox is studied as a zoonotic poxvirus disease which can occur in humans and other animals due to substitution of the amino acid serine with methionine. We investigate the (+)-catechin, betulinic acid, ursolic acid, quercetin-3-O-galactoside, luteolin-7-O-glucoside, and myricetin in Sarracenia [...] Read more.

In this article, monkeypox is studied as a zoonotic poxvirus disease which can occur in humans and other animals due to substitution of the amino acid serine with methionine. We investigate the (+)-catechin, betulinic acid, ursolic acid, quercetin-3-O-galactoside, luteolin-7-O-glucoside, and myricetin in Sarracenia purpurea drugs from Sarraceniaceae family for treating monkeypox disease. This is performed via adsorption onto the surface of (6,6) armchair single-walled carbon nanotube (SWCNT) at the B3LYP/6-311+G (2d,p) level of theory in a water medium as the drug delivery method at 300 K. Sarracenia purpurea has attracted much attention for use in the clinical treatment of monkeypox disease due to the adsorption of its effective compounds of (+)-catechin, betulinic acid, ursolic acid, quercetin-3-O-galactoside, luteolin-7-O-glucoside, and myricetin onto the surface of (6,6) armchair SWCNT, a process which introduces an efficient drug delivery system though NMR, IR and UV-VIS data analysis to the optimized structure. In addition to the lowering of the energy gap (∆E = E _LUMO − E_HOMO), HOMO–LUMO energy has illustrated the charge transfer interactions taking place within (+)-catechin, betulinic acid, ursolic acid, quercetin-3-O-galactoside, luteolin-7-O-glucoside, and myricetin. The atomic charges have provided the proper perception of molecular theory and the energies of fundamental molecular orbitals. Full article

(This article belongs to the Special Issue Computational Biology and High-Performance Computing)

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Graphical abstract

12 pages, 2414 KiB

Open AccessArticle

Development of Mathematical Model to Predict Soymilk Fouling Deposit Mass on Heat Transfer Surfaces Using Dimensional Analysis

by Eakasit Sritham, Navaphattra Nunak, Ekarin Ongwongsakul, Jedsada Chaishome, Gerhard Schleining and Taweepol Suesut

Computation 2023, 11(4), 83; https://doi.org/10.3390/computation11040083 - 18 Apr 2023

Cited by 1 | Viewed by 1255

Abstract

The formation of fouling deposits on heat exchanger surfaces is one of the major concerns in thermal processes. The fouling behavior of food materials is complex, and its mechanism remains, in general, unclear. This study was aimed at developing a predictive model for [...] Read more.

The formation of fouling deposits on heat exchanger surfaces is one of the major concerns in thermal processes. The fouling behavior of food materials is complex, and its mechanism remains, in general, unclear. This study was aimed at developing a predictive model for soymilk fouling deposit formed on heated surfaces using dimensional analysis. Relevant variables affecting fouling deposit mass could be grouped into six dimensionless terms using Buckingham’s pi-theorem. Experimental data were obtained from a lab-scale plate heat exchanger. A simple model developed using the experimental data under the process conditions with the product inlet temperature, the product outlet temperature, and plate surface temperature in the ranges of 50–55 °C, 65–70 °C, and 70–85 °C, respectively, exhibited a good performance in the prediction of soymilk fouled mass. The correlation coefficient between the predicted and experimental values of fouled mass was 0.97 with an average relative error of 9.03%. Within the ranges of product inlet temperature and plate surfaces temperature studied, this model offers an opportunity to estimate soymilk fouling mass with acceptable accuracy. Full article

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12 pages, 2703 KiB

Open AccessArticle

Effect of Passenger Physical Characteristics in the Uptake of Combustion Products during a Railway Tunnel Evacuation Due to a Fire Accident

by Thomas Zisis, Konstantinos Vasilopoulos and Ioannis Sarris

Computation 2023, 11(4), 82; https://doi.org/10.3390/computation11040082 - 14 Apr 2023

Cited by 1 | Viewed by 2092

Abstract

The current study examines how different types of passengers (elders, travelers with luggage, travelers without luggage, and mixed population) affect the evacuation process in railway tunnels after a fire accident based on Fractional Effective Dose (FED) index values. A 20 MW diesel pool [...] Read more.

The current study examines how different types of passengers (elders, travelers with luggage, travelers without luggage, and mixed population) affect the evacuation process in railway tunnels after a fire accident based on Fractional Effective Dose (FED) index values. A 20 MW diesel pool fire in an immobilized train located inside a straight, rectangular railroad tunnel that is ventilated by a longitudinal jet fan ventilation system is the scenario under consideration. Two fire scenarios were examined, one with and one without ventilation, combined with four evacuation scenarios. The numerical simulation of the fire and the evacuation process is conducted with the Fire Dynamics Simulator and Evacuation code (FDS + Evac) which is a Large Eddy Simulator (LES) for low-Mach thermally driven flows. The results (evacuation times, walking speeds, and mean and max FED values) are compared for each passenger type. It is found that during the evacuation from a railway tunnel fire accident, the most affected population are the elderly because of their lower movement speed, and travelers with luggage because of their increased dimensions. It is also shown that a non-homogenous population has increased uptake of combustion products and longer evacuation times than a homogenous population with similar geometrical characteristics. Full article

(This article belongs to the Special Issue Selected Papers from the 10th International Conference from Scientific Computing to Computational Engineering (IC-SCCE 2022))

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17 pages, 6304 KiB

Open AccessReview

Survey of Recent Deep Neural Networks with Strong Annotated Supervision in Histopathology

by Dominika Petríková and Ivan Cimrák

Computation 2023, 11(4), 81; https://doi.org/10.3390/computation11040081 - 14 Apr 2023

Viewed by 1861

Abstract

Deep learning (DL) and convolutional neural networks (CNNs) have achieved state-of-the-art performance in many medical image analysis tasks. Histopathological images contain valuable information that can be used to diagnose diseases and create treatment plans. Therefore, the application of DL for the classification of [...] Read more.

Deep learning (DL) and convolutional neural networks (CNNs) have achieved state-of-the-art performance in many medical image analysis tasks. Histopathological images contain valuable information that can be used to diagnose diseases and create treatment plans. Therefore, the application of DL for the classification of histological images is a rapidly expanding field of research. The popularity of CNNs has led to a rapid growth in the number of works related to CNNs in histopathology. This paper aims to provide a clear overview for better navigation. In this paper, recent DL-based classification studies in histopathology using strongly annotated data have been reviewed. All the works have been categorized from two points of view. First, the studies have been categorized into three groups according to the training approach and model construction: 1. fine-tuning of pre-trained networks for one-stage classification, 2. training networks from scratch for one-stage classification, and 3. multi-stage classification. Second, the papers summarized in this study cover a wide range of applications (e.g., breast, lung, colon, brain, kidney). To help navigate through the studies, the classification of reviewed works into tissue classification, tissue grading, and biomarker identification was used. Full article

(This article belongs to the Special Issue Computational Medical Image Analysis)

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4 pages, 183 KiB

Open AccessEditorial

Computational Issues in Insurance and Finance

by Cira Perna and Marilena Sibillo

Computation 2023, 11(4), 80; https://doi.org/10.3390/computation11040080 - 14 Apr 2023

Viewed by 877

Abstract

Comparison and cultural exchange always enrich and produce innovative and interesting results [...] Full article

(This article belongs to the Special Issue Computational Issues in Insurance and Finance)

15 pages, 2577 KiB

Open AccessArticle

Computational Investigation of Dental Implant Restoration Using Platform-Switched and -Matched Configurations

by Mohammad Afazal, Shubham Gupta, Abhishek Tevatia, Saba Afreen and Arnab Chanda

Computation 2023, 11(4), 79; https://doi.org/10.3390/computation11040079 - 12 Apr 2023

Cited by 2 | Viewed by 1653

Abstract

Dental trauma is a serious and highly prevalent health issue across the globe. Most of the frequent dental injuries result in the loss of teeth and affects the overall quality of life. The loss of a tooth is usually compensated by a dental [...] Read more.

Dental trauma is a serious and highly prevalent health issue across the globe. Most of the frequent dental injuries result in the loss of teeth and affects the overall quality of life. The loss of a tooth is usually compensated by a dental implant. The common methods adopted while placing the implant tooth are platform switching and platform matching. A plethora of works has studied the qualitative performance of these methods across different situations clinically. However, a detailed comparative work studying in-depth the mechanical parameters has not been attempted yet. In this computational work, two commonly available different platform-switched and one platform-matched implant-abutment configurations were compared. A 3D model of an implant (5.5 × 9.5 mm) was designed and inserted into a human mandibular bone block using computer-aided design (CAD) and extracting the clinical imaging data. Three separate models of implant-abutment configurations such as Platform Switched (PS)-I, a 5.5 mm implant with a 3.8 mm wide abutment, Platform Switched (PS)-II, a 5.5 mm implant with a 4.5 mm wide abutment, and Platform Matched (PM), a 5.5-mm implant with a 5.5 mm wide abutment were analyzed. Clinically relevant vertical-, horizontal-, and oblique-type of occlusal loadings were applied to each model to characterize the mechanical response. Mechanical parameters such as von Mises stresses, deformations, and strain energies were obtained using finite element modeling (FEM). These parameters showed lower values for platform switching within the peri-implant bone and that may help to limit marginal bone loss. However, the same parameters were increasing more in the abutment, implant, and screw for the platform-switched implant configuration than that of platform-matched configuration. The computational framework, along with the results, are anticipated to guide the clinicians and medical practitioners in making better decisions while selecting the commonly available methods. Full article

(This article belongs to the Special Issue Application of Finite Element Methods)

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19 pages, 5086 KiB

Open AccessArticle

Energy Consumption Monitoring System Based on IoT for Residential Rooftops

by Sarah El Himer, Mariyam Ouaissa, Mariya Ouaissa, Moez Krichen, Mohannad Alswailim and Mutiq Almutiq

Computation 2023, 11(4), 78; https://doi.org/10.3390/computation11040078 - 10 Apr 2023

Cited by 3 | Viewed by 3201

Abstract

This work aims to create a web-based real-time monitoring system for electrical energy consumption inside a specific residence. This electrical energy is generated from a micro-CPV system lying on the roof of this residence. The micro-CPV is composed of a Fresnel lens as [...] Read more.

This work aims to create a web-based real-time monitoring system for electrical energy consumption inside a specific residence. This electrical energy is generated from a micro-CPV system lying on the roof of this residence. The micro-CPV is composed of a Fresnel lens as the main optical element, a spherical lens as the secondary optical element, and a multi-junction solar cell. A tiny photovoltaic concentrator system with a geometric concentration ratio of 100× is analyzed in the first part of this study, while the second part is designed to monitor the electricity generated by the micro-CPV system. An ESP8266 controller chipset is used to build the sensing peripheral node, which controls a relay and a PZEM-004T current sensor. As a result, the optical element used has approximately 83% optical efficiency, with an acceptance angle of 1.5°. Regarding the monitoring system, the architecture demonstrates the ability of the system to monitor current and energy consumption in real time using a computer or smartphone and a web server specially designed to continuously update the power consumption profile in a specific smart home environment. The whole electric power consumption monitoring system generally worked well. The monitoring system is configured to provide excellent accuracy for a 0.6% hit. Full article

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18 pages, 5101 KiB

Open AccessArticle

Preliminary Design and Numerical Investigation of a Centrifugal Compressor for Supercritical Carbon Dioxide Operating in the Vicinity of Its Critical Thermodynamic State

by Georgios R. K. Aretis, Apostolos A. Gkountas, Dimitrios G. Koubogiannis and Ioannis E. Sarris

Computation 2023, 11(4), 77; https://doi.org/10.3390/computation11040077 - 08 Apr 2023

Viewed by 1567

Abstract

Waste heat recovery is one of the main practices used to reduce the carbon footprint of the industrial sector regarding environmental concern. The supercritical carbon dioxide (s-CO₂) cycle is one of the most attractive heat-to-power technologies; due to the abrupt variation [...] Read more.

Waste heat recovery is one of the main practices used to reduce the carbon footprint of the industrial sector regarding environmental concern. The supercritical carbon dioxide (s-CO₂) cycle is one of the most attractive heat-to-power technologies; due to the abrupt variation in CO₂ properties in the vicinity of its critical point, small compression work is required and finally a high cycle efficiency is achieved. In the literature, among the various proposed layouts, the recompression s-CO₂ Brayton cycle is considered to be the most efficient one. The most critical component of such a cycle is definitely the main compressor, as the related usual design procedures have been developed in the past for ideal gas as a working fluid. This study presents a methodology for the preliminary design of a centrifugal compressor with a vaned diffuser, suitable for fulfilling the desired operating requirements of a particular supercritical CO₂ recompression Brayton cycle. Furthermore, it demonstrates the numerical investigation of the three-dimensional (3D) flow phenomena occurring in it, focusing on the investigation of possible condensation. To this end, a one-dimensional flow model was developed to provide information regarding the geometry of the compressor and predict its prospective performance. Commercial computational fluid dynamics (CFD) software was then employed to examine the three-dimensional flow. The effect of accuracy in the evaluation of real gas properties approaching the critical point was examined, showing that a look-up table with more points around the critical point can reduce the numerical relative error by up to 0.3% for the value of specific heat capacity. In addition, the possibility of condensation occurrence was investigated at the impeller’s inlet, where the flow is accelerated. The supersaturation pressure ratio was defined and implemented in order to identify regions where static pressure is lower than saturation pressure, possibly leading to local two-phase flow. Full article

(This article belongs to the Section Computational Engineering)

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15 pages, 49865 KiB

Open AccessArticle

Pentaband Dual-Polarized Antenna for Multiservice Wireless Applications

by A. Ushasree and Vipul Agarwal

Computation 2023, 11(4), 76; https://doi.org/10.3390/computation11040076 - 08 Apr 2023

Cited by 1 | Viewed by 1358

Abstract

This paper presents a novel design for and an experimental study of a dual-polarized quad-port MIMO antenna. The design achieves resonance at five distinct frequency bands with reduced mutual coupling. The design includes a single annular ring slot, four truncated rectangular corners, and [...] Read more.

This paper presents a novel design for and an experimental study of a dual-polarized quad-port MIMO antenna. The design achieves resonance at five distinct frequency bands with reduced mutual coupling. The design includes a single annular ring slot, four truncated rectangular corners, and a truncated aperture to improve resonance behavior. The design is then extended to a four-port MIMO antenna by including a ground-plane slit to enhance isolation between antenna elements at the center resonance band. The antenna achieves resonances at 5 distinct bands, ranging from 1.5 to 8.4 GHz, with significant mutual coupling reductions. The resonances of the quad-port pentaband MIMO antenna are achieved at 1.55 GHz (1.5–1.65 GHz), 2.5 GHz (2.4–2.7 GHz), 5.2 GHz (5–5.85), 7.3 GHz (7.1–7.4), and 8.15 GHz (7.9–8.4), with respective mutual coupling reductions of 27 dB, 37 dB, 21 dB, 29 dB, and 21 dB. Additionally, the 3 dB axial ratio bandwidth (ARBW) is observed at 6.5% (1.5–1.6 GHz) and 15% (2.4–2.7 GHz) in 2 distinct bands, and the envelope correlation coefficient and diversity gain are calculated within the specified band range. Experimental measurements of the prototype for the quad-port antenna are conducted, with excellent agreement found between the results and the simulations. Full article

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17 pages, 2733 KiB

Open AccessFeature PaperArticle

Robust Stabilization of a Microgrid with Communication Delay and Uncertainties

by Ashraf Khalil, Asma Alfergani, Farhat M. Shaltami and Ali Asheibi

Computation 2023, 11(4), 75; https://doi.org/10.3390/computation11040075 - 07 Apr 2023

Cited by 2 | Viewed by 1593

Abstract

In this paper, the robust stabilization for the networked microgrid system is presented. A microgrid implements master-slave control architecture where the communication channel is utilized to exchange the reference current signals. With this structure, a time delay exists in the reference control signal [...] Read more.

In this paper, the robust stabilization for the networked microgrid system is presented. A microgrid implements master-slave control architecture where the communication channel is utilized to exchange the reference current signals. With this structure, a time delay exists in the reference control signal which may lead to instability. The analysis of the control strategy is carried out in dq reference frame. The microgrid is constituted by PV and wind energy sources supplying a load through voltage source inverters. The stochastic nature of renewable energy sources introduces uncertainties which can be represented as fluctuations in the voltage and the current. The main contribution of the paper is formulating the controller design of the microgrid with communication delay and uncertainties in the model as H∞ control problem and Lyapunov–Krasovskii functional is utilized to develop stability criterion in bilinear matrix inequality form. Grey wolf optimizer is used to minimize the performance index and derive the stabilizing controller. The microgrid performance is tested through simulation using the time-varying nonlinear model of the microgrid. The results prove that satisfactory current and power-sharing are attained even with the existence of time delays and uncertainties. Full article

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14 pages, 4194 KiB

Open AccessArticle

Modification of the Bellman–Ford Algorithm for Finding the Optimal Route in Multilayer Network Structures

by Olga Timofeeva, Alexey Sannikov, Maria Stepanenko and Tatiana Balashova

Computation 2023, 11(4), 74; https://doi.org/10.3390/computation11040074 - 07 Apr 2023

Viewed by 1951

Abstract

One of the actual tasks of the contemporary logistics business using the “just in time” supply planning concept, is to distribute manufactured goods among the objects of the distribution network in the most efficient manner at the lowest possible cost. The article is [...] Read more.

One of the actual tasks of the contemporary logistics business using the “just in time” supply planning concept, is to distribute manufactured goods among the objects of the distribution network in the most efficient manner at the lowest possible cost. The article is devoted to the problem of finding the optimal path in network structures. The problem statement for multilayer data transmission networks (MDTN), which is one of the possible representations of multimodal transport networks, is considered. Thus, each MDTN layer can be represented as a separate type of transport. The problem is solved by modifying the Bellman–Ford mathematical programming algorithm. Load testing of the modified method was performed, and a comparative analysis was given, including an assessment of speed and performance, proving the effectiveness of the results of the study. Based on the results of comparative analysis, recommendations for using a modified version of the Bellman–Ford algorithm for application in practical problems in optimizing logistics networks are proposed. The results obtained can be used in practice not only in logistics networks but also in the construction of smart energy networks, as well as in other subject areas that require optimization of multilayer graph structures. Full article

(This article belongs to the Special Issue Transport and Logistics Optimization Solution)

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18 pages, 735 KiB

Open AccessArticle

A Comprehensive Decision Framework for Selecting Distribution Center Locations: A Hybrid Improved Fuzzy SWARA and Fuzzy CRADIS Approach

by Adis Puška, Anđelka Štilić and Željko Stević

Computation 2023, 11(4), 73; https://doi.org/10.3390/computation11040073 - 02 Apr 2023

Cited by 4 | Viewed by 1573

Abstract

The focus of this study is on the significance of location in establishing distribution centers. The key question when selecting a location is regarding which location would contribute the most to the growth of a company’s business through the establishment of distribution centers. [...] Read more.

The focus of this study is on the significance of location in establishing distribution centers. The key question when selecting a location is regarding which location would contribute the most to the growth of a company’s business through the establishment of distribution centers. To answer this question, we conducted research in the Brčko District of BiH in order to determine the best location for a distribution center using expert decision-making based on linguistic values. In order to use these values when selecting locations, a fuzzy set was formed using the IMF SWARA (Improved Fuzzy Stepwise Weight Assessment Ratio Analysis) and fuzzy CRADIS (Compromise Ranking of Alternatives from Distance to the Ideal Solution) methods. The IMF SWARA method was utilized to determine the weights of the criteria, and the fuzzy CRADIS method was employed to rank the locations based on expert ratings. The location for the construction of distribution centers at Bodarište was rated the worst, while the McGowern Base location was rated the best. Based on these findings, the research question was answered, and it was demonstrated that fuzzy methods could be utilized in the selection of distribution center locations. Hence, we recommend that future research be performed on the application of fuzzy methods in the expert selection of potential sites for distribution centers. Full article

(This article belongs to the Special Issue Transport and Logistics Optimization Solution)

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18 pages, 5841 KiB

Open AccessArticle

A Robust Bubble Growth Solution Scheme for Implementation in CFD Analysis of Multiphase Flows

by Hao Pang and Gracious Ngaile

Computation 2023, 11(4), 72; https://doi.org/10.3390/computation11040072 - 31 Mar 2023

Viewed by 1361

Abstract

Although the full form of the Rayleigh–Plesset (RP) equation more accurately depicts the bubble behavior in a cavitating flow than its reduced form, it finds much less application than the latter in the computational fluid dynamic (CFD) simulation due to its high stiffness. [...] Read more.

Although the full form of the Rayleigh–Plesset (RP) equation more accurately depicts the bubble behavior in a cavitating flow than its reduced form, it finds much less application than the latter in the computational fluid dynamic (CFD) simulation due to its high stiffness. The traditional variable time-step scheme for the full form RP equation is difficult to be integrated with the CFD program since it requires a tiny time step at the singularity point for convergence and this step size may be incompatible with time marching of conservation equations. This paper presents two stable and efficient numerical solution schemes based on the finite difference method and Euler method so that the full-form RP equation can be better accepted by the CFD program. By employing a truncation bubble radius to approximate the minimum bubble size in the collapse stage, the proposed schemes solve for the bubble radius and wall velocity in an explicit way. The proposed solution schemes are more robust for a wide range of ambient pressure profiles than the traditional schemes and avoid excessive refinement on the time step at the singularity point. Since the proposed solution scheme can calculate the effects of the second-order term, liquid viscosity, and surface tension on the bubble evolution, it provides a more accurate estimation of the wall velocity for the vaporization or condensation rate, which is widely used in the cavitation model in the CFD simulation. The legitimacy of the solution schemes is manifested by the agreement between the results from these schemes and established ones from the literature. The proposed solution schemes are more robust in face of a wide range of ambient pressure profiles. Full article

(This article belongs to the Section Computational Engineering)

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23 pages, 8445 KiB

Open AccessArticle

Online Multiscale Finite Element Simulation of Thermo-Mechanical Model with Phase Change

by Dmitry Ammosov and Maria Vasilyeva

Computation 2023, 11(4), 71; https://doi.org/10.3390/computation11040071 - 29 Mar 2023

Cited by 2 | Viewed by 1391

Abstract

This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur due to [...] Read more.

This paper presents a thermo-mechanical model with phase transition considering changes in the mechanical properties of the medium. The proposed thermo-mechanical model is described by a system of partial differential equations for temperature and displacements. In the model, soil deformations occur due to porosity growth caused by ice and water density differences. A finite-element approximation of this model on a fine grid is presented. The linearization from the previous time step is used to handle the nonlinearity of the problem. For reducing the size of the discrete problem, offline and online multiscale approaches based on the Generalized Multiscale Finite Element Method (GMsFEM) are proposed. A two-dimensional model problem simulating the heaving process of heterogeneous soil with a stiff inclusion was considered for testing the mathematical model and the multiscale approaches. Numerical solutions depict the process of soil heaving caused by changes in porosity due to the phase transition. The movement of the phase transition interface was observed. The change of medium properties, including the elastic modulus, was traced and corresponds to the phase transition interface. The proposed multiscale approaches significantly reduce the size of the discrete problem while maintaining reasonable accuracy. However, the online multiscale approach achieves better accuracy than the offline approach with fewer degrees of freedom. Full article

(This article belongs to the Special Issue Application of Finite Element Methods)

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12 pages, 506 KiB

Open AccessArticle

Some Properties of the Computation of the Modular Inverse with Applications in Cryptography

by Michele Bufalo, Daniele Bufalo and Giuseppe Orlando

Computation 2023, 11(4), 70; https://doi.org/10.3390/computation11040070 - 27 Mar 2023

Cited by 1 | Viewed by 1718

Abstract

In the field of cryptography, many algorithms rely on the computation of modular multiplicative inverses to ensure the security of their systems. In this study, we build upon our previous research by introducing a novel sequence,

{(z_{j})}_{j \geq 0}

[...] Read more.

In the field of cryptography, many algorithms rely on the computation of modular multiplicative inverses to ensure the security of their systems. In this study, we build upon our previous research by introducing a novel sequence,

{(z_{j})}_{j \geq 0}

, that can calculate the modular inverse of a given pair of integers

(a, n)

, i.e.,

a^{- 1}; m o d, n

. The computational complexity of this approach is

O (a)

, which is more efficient than the traditional Euler’s phi function method,

O (n, \ln, n)

. Furthermore, we investigate the properties of the sequence

{(z_{j})}_{j \geq 0}

and demonstrate that all solutions of the problem belong to a specific set,

I

, that only contains the minimum values of

{(z_{j})}_{j \geq 0}

. This results in a reduction of the computational complexity of our method, especially when

a \sim n

and it also opens new opportunities for discovering closed-form solutions for the modular inverse. Full article

(This article belongs to the Section Computational Engineering)

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25 pages, 1116 KiB

Open AccessArticle

The Multi-Maximum and Quasi-Maximum Common Subgraph Problem

by Lorenzo Cardone and Stefano Quer

Computation 2023, 11(4), 69; https://doi.org/10.3390/computation11040069 - 27 Mar 2023

Cited by 1 | Viewed by 1488

Abstract

The Maximum Common Subgraph problem has been long proven NP-hard. Nevertheless, it has countless practical applications, and researchers are still searching for exact solutions and scalable heuristic approaches. Driven by applications in molecular science and cyber-security, we concentrate on the Maximum Common Subgraph [...] Read more.

The Maximum Common Subgraph problem has been long proven NP-hard. Nevertheless, it has countless practical applications, and researchers are still searching for exact solutions and scalable heuristic approaches. Driven by applications in molecular science and cyber-security, we concentrate on the Maximum Common Subgraph among an indefinite number of graphs. We first extend a state-of-the-art branch-and-bound procedure working on two graphs to N graphs. Then, given the high computational cost of this approach, we trade off complexity for accuracy, and we propose a set of heuristics to approximate the exact solution for N graphs. We analyze sequential, parallel multi-core, and parallel-many core (GPU-based) approaches, exploiting several leveraging techniques to decrease the contention among threads, improve the workload balance of the different tasks, reduce the computation time, and increase the final result size. We also present several sorting heuristics to order the vertices of the graphs and the graphs themselves. We compare our algorithms with a state-of-the-art method on publicly available benchmark sets. On graph pairs, we are able to speed up the exact computation by a 2× factor, pruning the search space by more than 60%. On sets of more than two graphs, all exact solutions are extremely time-consuming and of a complex application in many real cases. On the contrary, our heuristics are far less expensive (as they show a lower-bound for the speed up of 10×), have a far better asymptotic complexity (with speed ups up to several orders of magnitude in our experiments), and obtain excellent approximations of the maximal solution with 98.5% of the nodes on average. Full article

(This article belongs to the Special Issue Graph Theory and Its Applications in Computing)

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