Complex Calculations Research Articles

ОЦІНКА ОБЧИСЛЮВАЛЬНОЇ СКЛАДНОСТІ ГЕНЕТИЧНОГО АЛГОРИТМУ

The article is devoted to the estimation of computational complexity of a genetic algorithm as one of the key tools for solving optimisation problems. The theoretical aspects of computational complexity of algorithms and the interrelation of elements of a genetic algorithm are considered. The main types of computational complexity of algorithms are described: time, simple and asymptotic. Five basic rules for calculating the asymptotic complexity are given. A mathematical apparatus for estimating the asymptotic complexity of a genetic algorithm is presented, which takes into account the costs of forming the initial population and performing evolution. Evolution occurs through iterations, during which generations of individuals are subjected to certain operations in order to find an optimal solution (crossing, mutation, chromosome decoding, etc.). GA, as a global search algorithm, is considered to find the optimal path without getting stuck in local minima. To assess the computational complexity of GA, we consider solving the traveling salesman problem (TSP) for 28 cities of Ukraine using a modified TSPLIB library and the DEAP platform created in the Python programming language. A block diagram of the GA is presented, the main elements of which are the tournament selection operator, the ordered crossover operator, and the inversion mutation operator. The influence of the population size and the number of generations on the asymptotic complexity of the genetic algorithm in solving the TSP problem is studied. The study considered changing the size of the GA population from 50 to 500 with a step of 50, while for each such value four sets of the number of generations were modelled: from 50 to 200 with a step of 50. Based on the obtained results, we show a linear dependence of the GA execution time on the size of the considered input data. It is shown that the smallest time complexity of the presented GA for the given TSP problem is 0.33848 seconds with a population size of 50 and a similar number of generations, while the largest value is 3.752734 seconds with a population size of 500 and a number of generations of 200. The obtained results can be used to optimise the performance of a GA in the TSP problem.

Application of self-learning interval type-2 fuzzy neural network in PM2.5 concentration prediction

Abstract The change of PM2.5 concentration in air quality is nonlinear and difficult to predict. Therefore, a self-learning interval type-2 fuzzy neural network (SLIT2FNN) is proposed. SLIT2FNN has two parts: online structure learning and parameter learning. In structure learning, to improve the training accuracy and speed of the model, the Possibilistic Fuzzy C-Means (PFCM) algorithm is used to process the input data and obtain the number of initial rules before model training. The PFCM algorithm introduces the concept of possibility P to Fuzzy C-Means (FCM), allowing PFCM to overcome the shortcomings of FCM that cannot accurately cluster a large number of nonlinear problems. SLIT2FNN can establish an appropriate number of rules in the preparation stage, and then use the firing strength of the antecedents of the rules to judge whether to generate fuzzy rules for online self-learning, thereby optimizing its network structure. Then, the improved Levenberg–Marquardt (ILM) algorithm is used to modify the relevant parameters of SLIT2FNN. The ILM algorithm can address the challenge of numerous parameters in the Jacobian matrix and complex calculations and improve the calculation speed and adaptive ability of SLIT2FNN parameter learning. Finally, SLIT2FNN is applied to the prediction of air quality PM2.5 concentration, and the performance is compared with other models. The experiment proves that SLIT2FNN has a high prediction accuracy and fast convergence.

ANN based Fire Resistance Prediction of FRP-Strengthened RC Slabs with Fireproof Panel Including Air Layer

In this study, an Artificial Neural Network (ANN) model to predict the fire resistance of Fiber Reinforced Plastic (FRP) strengthened Reinforced Conrete (RC) slabs with fireproof panel including air layer exposed to fire is developed. FRP-strengthened RC slabs with fireproof panel including air layer has a structure that improves structural performance and fire resistance by placing FRP and a fireproof panel including air at the bottom of the RC slab. First, fire test is performed using the air layer as a variable, and the validity of the software ABAQUS heat transfer analysis is verified by comparing it with the fire test results. Through this heat transfer analysis, the temperature distribution of the slab is determined, and 1521 data sets are obtained by calculating the strength reduction coefficient and elastic coefficient reduction coefficient of each material. The data consist of eight input parameters: the type of fire curve, fire exposure time, insulation thickness, air layer thickness, concrete covering thickness, and FRP thickness. The output parameter is the value of the strength and elastic modulus reduction coefficient for each material. The average values of MSE, RMSE, R, and SSE for all output parameters, which are performance indicators of the ANN model, are 0.00202, 0.03978, 0.98235, and 1.10445, respectively, and the developed ANN model has high computational accuracy and high generalization ability. Therefore, the ANN model developed here can determine the mechanical properties of each material in FRP-strengthened RC slabs with fireproof panel including air layer exposed to fire and evaluate the fire resistant without complex calculations. Through contribution and sensitivity analysis, the effect of input data on output data is confirmed.

ML-Aided Computational Screening of 2D Materials for Photocatalytic Water Splitting.

The exploration of two-dimensional (2D) materials with exceptional physical and chemical properties is essential for the advancement of solar water splitting technologies. However, the discovery of 2D materials is currently heavily reliant on fragmented studies with limited opportunities for fine-tuning the chemical composition and electronic features of compounds. Starting from the V2DB digital library as a resource of 2D materials, we set up and execute a funnel approach that incorporates multiple screening steps to uncover potential candidates for photocatalytic water splitting. The initial screening step is based upon machine learning (ML) predicted properties, and subsequent steps involve first-principles modeling of increasing complexity, going from density functional theory (DFT) to hybrid-DFT to GW calculations. Ensuring that at each stage more complex calculations are only applied to the most promising candidates, our study introduces an effective screening methodology that may serve as a model for accelerating 2D materials discovery within a large chemical space. Our screening process yields a selection of 11 promising 2D photocatalysts.

Accurate and Efficient Simulation Models for Power Electronics Transformers Based on Series-Connected Active Unity Power Factor Rectifier Modules

This paper contributes an efficient simulation technique for input-series output-parallel multilevel power electronics transformers based on active unity-power-factor rectifiers as building blocks. The technical motivation of the work comes from the fact that the computational burden for the simulation of these technologies tends to become unaffordable as the number of modules grows when using commercial software blocksets. This paper presents a new method to drastically reduce the simulation complexity by simplifying the switching rules: in a three-phase circuit, each phase zero-crossing condition is implemented by a single and simple algebraic rule, so the complex calculations for determining the conduction state of each single diode are removed from the model. The computational enhancement and accuracy of the proposed technique are proved by experimental verification using a single-phase single-cell prototype together with multiple simulations of full-scale systems of different sizes.

Fall Detection System based on iOS Smartphone Sensors

Activities of daily living (ADLs) are a crucial aspect of human life, especially in remote health monitoring and fall detection. As smartphones have become an integral part of our daily routines, with their ability to perform complex calculations, connect to the internet, and incorporate various sensors, researchers have been inspired to explore human activity recognition systems. This paper focuses on accelerometer and gyroscope data from iOS-based smartphones. We developed a data collection app to record fall types (e.g., Falling Right, Falling Left) and fall-like activities (e.g., Sitting Fast, Jumping). Volunteers carried smartphones naturally in their pockets during experiments, presenting a challenge of noise but enhancing user comfort. We applied different Machine Learning algorithms (Decision Trees, Random Forest, Logistic Regression, k-Nearest Neighbor, XGBoost, LightGBM, and Neural Networks) to analyze the collected dataset. In contrast to typical studies, our approach replicated real-world smartphone usage. The paper presents and analyzes promising results from the study. Furthermore, we implemented the trained model as a real-time mobile application for potential users. This research illustrates the potential of smartphones in fall detection and opens the way for user-friendly solutions in remote health monitoring.

Establishment of a Reference Evapotranspiration Forecasting Model Based on Machine Learning

Water scarcity is a global problem. Deficit irrigation (DI) reduces evapotranspiration, improving water efficiency in agriculture. Reference evapotranspiration (ET0) is an important factor in determining DI. ET0 forecasting predicts field water consumption and enables proactive irrigation decisions, offering guidance for water resource management. However, implementation of ET0 forecasting faces challenges due to complex calculations and extensive meteorological data requirements. This project aims to develop a machine learning system for ET0 forecasting. The project involves studying ET0 methods and identifying required meteorological parameters. Historical meteorological data and weather forecasts were obtained from meteorological websites and analyzed for accuracy after preprocessing. A machine learning-based model was created to forecast reference crop evapotranspiration. The model’s input parameters were selected through path analysis before it was optimized using Bayesian optimization to reduce overfitting and improve accuracy. Three forecasting models were developed: one based on historical meteorological data, one based on weather forecasts, and one that corrects the weather forecasts. All three models achieved good accuracy, with root mean square errors ranging from 0.52 to 0.81 mm/day. Among them, the model based on weather forecast had the highest accuracy; the RMSE six days before the forecast period was between 0.52 and 0.75 mm/day, and the RMSE on the seventh day of the forecast period was 1.12 mm/day. In summary, this project has established a mathematical model of ET0 prediction based on machine learning, which can achieve more accurate predictions for within a few days.

Maximisation the autonomous flight performance of unmanned helicopter using BSO algorithm

Abstract The usage areas of rotary or fixed wing unmanned aerial vehicles (UAV) have become very widespread with technological developments. For this reason, UAV designs differ in terms of aerodynamic design, flight performance and endurance depending on the intended use. In this study, maximising of the autonomous flight performance of the unmanned helicopter produced at Erciyes University using an optimisation algorithm is discussed. For this purpose, the input parameters of the dynamic model are chosen as blade length, blade mass density, blade chord width and blade twist angle of the unmanned helicopter and the proportional, integral, derivative gain coefficients of the lateral axis of the autopilot. The output parameters of the dynamic model are selected as settling time, rise time and maximum overshoot, which are autonomous performance parameters. The dynamic model consisting of helicopter and autopilot parameters is integrated into the back-tracking search optimisation (BSO) algorithm as an objective function. In the optimization process, where mean squared error (MSE) is used as the performance criterion, optimum input and output values were determined. Thus, helicopter and autopilot parameters, which are among the factors affecting autonomous performance, are taken into account with equal importance and simultaneously. Simulations show that the obtained values are satisfactory. With this approach based on the optimisation method, complex and time-consuming dynamic model calculations are reduced, time and cost are saved, and practicality is achieved in applications. Therefore, this approach can be an innovative and alternative method to improve UAV designs and increase flight performance compared to classical methods.

An Improved Fourier-Based Method for Path Generation of Planar Four-Bar Linkages without Prescribed Timing

Four-bar linkages are critical fundamental elements of many mechanical systems, and their design synthesis is often mathematically complicated with iterative numerical solutions. Analytical methods based on Fourier coefficients can circumvent these difficulties but have issues with time parameters assignment for path generation without prescribed time in previous studies. In this paper, an improved Fourier-based point-to-point combination method is presented, which generates more points by Fourier approximation and assigns the time parameters to the given points while allowing discarding solutions with order defects. This method relies on the Fourier coefficients, improving the accuracy of synthesis solutions, and simplifying the computational procedure. Time parameters are assigned directly to the given points, which avoids the complex calculations to find intersection points in the given path, eliminates combinations that would lead to solutions with order defects, and simplifies the assessment process of synthesis results. The parameters obtained by the point-to-point combination method can be used as the parameters of the input dyad, skipping the first set of design equations for faster calculation. Several examples are presented to demonstrate the advantages of the proposed synthesis method, which is easy-understanding, computationally efficient, and yields more accurate solutions than available synthesis methods.

Time-Controlled Authentication Strategies for Molecular Information Transfer.

Modern cryptography based on computational complexity theory is mainly constructed with silicon-based circuits. As DNA nanotechnology penetrates the molecular domain, utilizing molecular cryptography for data access protection in the biomolecular domain becomes a unique approach to information security. However, building security devices and strategies with robust security and compatibility is still challenging. Here, this study reports a time-controlled molecular authentication strategy using DNAzyme and DNA strand displacement as the basic framework. A time limit exists for authorization and access, and this spontaneous shutdown design further protects secure access. Multiple hierarchical authentications, temporal Boolean logic authentication, and enzyme authentication strategies are constructed based on DNA networks'good compatibility and programmability. This study gives proof of concept for the detection and protection of bioinformation about single nucleotide variants and miRNA, highlighting their potential in biosensing and security protection.

Correcting the Location Error of Persistent Scatterers in an Urban Area Based on Adaptive Building Contours Matching: A Case Study of Changsha

Persistent Scatterer InSAR (PS-InSAR) technology enables the monitoring of displacement in millimeters. However, without the use of external parameter correction, radar scatterers exhibit poor geopositioning precision in meters, limiting the correlation between observed deformation and the actual structure. The integration of PS-InSAR datasets and building databases is often overlooked in deformation research. This paper presents a novel strategy for matching between PS points and building contours based on spatial distribution characteristics. A convex hull is employed to simplify the building outline. Considering the influence of building height and incident angle on geometric distortion, an adaptive buffer zone is established. The PS points on a building are further identified through the nearest neighbor method. In this study, both ascending and descending TerraSAR-X orbit datasets acquired between 2016 and 2019 were utilized for PS-InSAR monitoring. The efficacy of the proposed method was evaluated by comparing the PS-InSAR results obtained from different orbits. Through a process of comparison and verification, it was demonstrated that the matching effect between PS points and building contours was significantly enhanced, resulting in an increase of 29.2% in the number of matching PS points. The results indicate that this novel strategy can be employed to associate PS points with building outlines without the need for complex calculations, thereby providing a robust foundation for subsequent building risk assessment.

BiGNN: Bipartite graph neural network with attention mechanism for solving multiple traveling salesman problems in urban logistics

The multiple traveling salesman problems (MTSP), which arise from real world problems, are essential in urban logistics. Variations such as MinMax-MTSP and Bounded-MTSP aim to distribute workload evenly among salesmen and impose constraints on visited cities, respectively. Branch-and-bound (B&B) provides an exact algorithm solution for these problems. The Learn to Branch (L2B) approach guides branch node selection through deep learning. In this study, we utilize mathematical modeling of Bipartite Graph Neural Network (BiGNN) and an attention mechanism to support B&B in exploring solution spaces through imitation learning. The problems are framed to formulate mixed integer linear programming, which is different from conventional algorithms. It is proposed that a bipartite graph network approach makes a feature representation by setting a structure of constraints and variables. Experimental results showed that our model can generate more accurate solutions than three benchmark models. The BiGNN model can effectively learn the strong branch strategy, which reduces solution time by replacing complex calculations with fast approximations. Additionally, the small-scale instances model can be applied to larger-scale ones.

Numerical simulation of an extensible capsule using regularized Stokes kernels and overset finite differences

In this paper, we present a novel numerical scheme for simulating deformable and extensible capsules suspended in a Stokesian fluid. The main feature of our scheme is a partition-of-unity (POU) based representation of the surface that enables asymptotically faster computations compared to spherical-harmonics based representations. We use a boundary integral equation formulation to represent and discretize hydrodynamic interactions. The boundary integrals are weakly singular. We use the quadrature scheme based on the regularized Stokes kernels by Tlupova and Beale 2019 (given in [34]). We also use partition-of unity based finite differences that are required for the computation of interfacial forces. Given an N-point surface discretization, our numerical scheme has fourth-order accuracy and O(N) asymptotic complexity, which is an improvement over the O(N2log⁡N) complexity of a spherical harmonics based spectral scheme that uses product-rule quadratures by Veerapaneni et al. 2011 [36]. We use GPU acceleration and demonstrate the ability of our code to simulate the complex shapes with high resolution. We study capsules that resist shear and tension and their dynamics in shear and Poiseuille flows. We demonstrate the convergence of the scheme and compare with the state of the art.

A study on secured encryption of medical images using significant visual cryptography

The medical images of people are important and sensitive and cannot be shared with the public considering privacy measures. Maintaining the confidentiality of the medical image is essential, and leakage of such information can cause great loss. Therefore, the information has to be secured while being transferred through a third party, which can be any network medium. Thus, there is a need for developing a robust encryption algorithm. These algorithms improve the security of the ongoing pictures by compromising the nature of the picture and utilizing complex calculations. Algorithms that work on the nature of the picture by utilizing complex cycles, for example, error diffusion, halftoning, wavelet transform, and dithering, lead to time complexity. Thus, a compact and efficient cryptographic algorithm is proposed with fewer mathematical computations that ensure the secured transmission and reception of medical images through the medium using Significant Visual Cryptography (SVC). In SVC, initially, the quality of the secret images (SI) is improved by using the Error Abatement Technique (EAT). The output of EAT is used to generate random share values, which are then implanted in cover pictures. The shares that are transmitted do not reveal the secret information present in the original image because of the steganography features involved in this technique. The integrated check value (ICV) is calculated over the region of interest (ROI) at the encryption and decryption sides to provide additional security. Quality and security analyses have been carried out to ensure the robustness of the algorithm. The detailed study proved that the proposed algorithm beat the constraints of the current calculations. The concept of checking the integrity value and steganography features enhanced the effectiveness of the algorithm.

Studying the Internal Wave Generation Mechanism in the Northern South China Sea Using Numerical Simulation, Synthetic Aperture Radar, and In Situ Measurements

The internal waves in the South China Sea are highly correlated with the tidal currents in the Luzon Strait, which makes it possible to establish an internal wave prediction model based on internal wave kinematics. However, the kinematic model requires the input of the exact location and time of the initial internal wave for which the generation mechanism of internal waves in the northern South China Sea must be well understood. By analyzing the internal wave field in the northern South China Sea (SCS) simulated using the MIT General Circulation Model (MITgcm) and observations from satellite synthetic aperture radar (SAR) and mooring temperature–salinity–depth (TSD) chains, the source regions and propagation initiation times of internal waves are identified for three typical tidal phases, i.e., the diurnal-tide-dominated phase (DTP), transition tide phase (TTP), and semidiurnal-tide-dominated phase (STP). The generation procedures of Type A and Type B internal waves are discussed in detail with those data. The present study reveals that Type A and Type B waves are generated at the eastern and western ridges, respectively, and both commence their westward propagation at the peak of the eastward tidal flow. The dynamics of lee waves and the resonance effect with double ridges constitute the generation mechanisms of internal waves in the northern SCS. Combined with varying configurations of tidal conditions, topography, and stratification, the generation procedures of Type A and Type B waves in the DTP, TTP, and STP are elucidated with the generation mechanism in a unified and self-consistent way. In short, during DTP, weaker A waves alternate with weaker B waves each day; during TTP, strong A waves and strong B waves appear alternately every day; and there are two weak A waves per day during the STP. The generation mechanism can help in developing future empirical models for generating internal waves using tidal currents, topography, and stratification without requiring complex fluid dynamics calculations.

Exploring Types of Photonic Neural Networks for Imaging and Computing-A Review.

Photonic neural networks (PNNs), utilizing light-based technologies, show immense potential in artificial intelligence (AI) and computing. Compared to traditional electronic neural networks, they offer faster processing speeds, lower energy usage, and improved parallelism. Leveraging light's properties for information processing could revolutionize diverse applications, including complex calculations and advanced machine learning (ML). Furthermore, these networks could address scalability and efficiency challenges in large-scale AI systems, potentially reshaping the future of computing and AI research. In this comprehensive review, we provide current, cutting-edge insights into diverse types of PNNs crafted for both imaging and computing purposes. Additionally, we delve into the intricate challenges they encounter during implementation, while also illuminating the promising perspectives they introduce to the field.

SMS2DC: Synchronous mobile sinks scheduling for data collection in internet of things‐enabled wireless sensor networks

SummaryEnergy‐efficient data collection in wireless sensor networks (WSNs) is crucial due to the limited battery capacity of sensor nodes (SNs). Using a mobile sink (MS) for data collection can lower the energy consumption of SNs to avoid relaying in WSNs. However, a single MS is not a feasible solution for large‐scale WSNs, so it was necessary to use multiple MSs to collect data. A synchronous MS scheduling strategy for data collection (SMS2DC) is proposed in this paper, which uses two types of MS, a local MS to collect data from SN and a global MS to collect data from local MS. In this process, we begin by partitioning the network based on chemical reaction optimization. For each partition, a MS is assigned and scheduled using a path construction strategy according to a geometric path construction approach. In addition, a global MS is scheduled based on a local MS trajectory by identifying the most appropriate collision point to collect data. As a result, the algorithm increases data collection accuracy while minimizing network data loss. The asymptotic time complexity of the proposed SMS2DC algorithm needed . The comparison results show the superiority of the proposed SMS2DC strategy under multiple scenarios under various deployment conditions.

Analysis of Spatial Curved Bi-Fixed Beam with Varying Curvature and Varying Cross-Sectional Area Using Finite Displacement Transfer Method

This article is focused on determination of fixed-end reactions, displacements, internal forces and internal moments for the spatial curved bi-fixed beam with varying curvature and varying cross-sectional area. The objective is to analyze spatially curved beam without involving analytical differentiation and integration of the governing equations. A finite displacement transfer method to analyze spatially curved beam is used to obtain numerically approximate analysis results and to eliminate analytical differentiation and integration, completely. The results of the analysis procedure are compared with the results of other methods found in the literature. For the specific case of the circular helical beam, the fixed end reactions' values have absolute maximum and minimum percentage differences of 1.23% and 0.06%, respectively. For the specific case of the elliptic-helical beam, the fixed end reactions' values have absolute maximum and minimum percentage differences of 1.13% and 0.0%, respectively. The finite difference method, along with the recursive scheme, gives reasonably accurate results without involving complex calculations

A DC fault current fast-computing method of MMC-HVDC grid with short circuit protection equipment

The multi-terminal modular multi-level converter-based high voltage direct current (MMC-HVDC) grid with short circuit protection equipment (SCPE) is so complex that it is difficult to estimate its fault current and analyze the performance of SCPE by conventional time-domain numerical calculation method, it meets three big obstacles. This paper has made significant progress in overcoming these obstacles. 1). By applying the modern electrical circuit theory, a systematic formulation of the differential equation set for fault current calculation is developed to avoid a lot of complex and cumbersome matrix manual calculations. 2). A novel Y-Delta transformation in the s-domain is proposed to develop an eliminating virtual node approach for a complex MMC-HVDC grid, including the ring, radial, and hybrid topologies. 3). It is difficult to solve the equivalent circuit of MMC-HVDC grid with SCPE since SCPE is a time-variable-nonlinear circuit. A canonical voltage source model of SCPE is established to transform the time-variable-nonlinear circuit into a piecewise linear circuit. Based on the three significant progresses, a DC fault current fast-computing method of MMC-HVDC grid with SCPE is put forward to deal with all kinds of MMC-HVDC grids with several kinds of SCPEs. Then, the performance of several kinds of SCPE is analyzed and compared by this method. Consequently, the proposed DC fault current fast-computing method is a new powerful tool to estimate the fault current of MMC-HVDC grid and analyze the performance of SCPE.

ET cool home: innovative educational activities on evapotranspiration and urban heat

Abstract. Teaching evapotranspiration (ET) in university courses often focuses on either oversimplified process descriptions or complex empirical calculations, both of which lack grounding in students' real-world experiences and prior knowledge. This calls for a more applied approach to teaching about ET that connects concepts to experience for improved educational outcomes. One such opportunity exists at the intersections between ET and heat in cities, where a growing majority of the world's population lives, including many of our students. In this work we describe an ET educational activity that integrates theory with practical design, taking advantage of the close link between ET processes and urban heat patterns. In a benchtop experiment, students measure ET variations across common land surfaces (e.g., asphalt, grass, and mulch) through water and energy balance approaches. The experiment is paired with an “urban heat tour” in the campus environment, facilitated by portable infrared cameras, offering firsthand observation of urban heat patterns. These two activities, together, provide context in which students can understand the difference in ET across various land covers, describe the relationship between ET and land surface temperatures, and explain the impacts of urban design on heat dynamics. The activities are adaptable to serve a diversity of student backgrounds and to different educational contexts, including public demonstrations and pre-university classrooms.