Sum Of Squared Errors Research Articles

Predicting stock market crashes on the African stock markets: evidence from log-periodic power law model

PurposeThis study aims to predict stock market crashes identified by the CMAX approach (current index level relative to historical maximum) during periods of global and local events, namely the subprime crisis of 2008, the political and social instability of 2011 and the COVID-19 pandemic.Design/methodology/approachOver the period 2004–2020, a log-periodic power law model (LPPL) has been employed which describes the price dynamics preceding the beginning dates of the crisis. In order to adjust the LPPL model, the Global Search algorithm was developed using the “fmincon” function.FindingsBy minimizing the sum of square errors between the observed logarithmic indices and the LPPL predicted values, the authors find that the estimated parameters satisfy all the constraints imposed in the literature. Moreover, the adjustment line of the LPPL models to the logarithms of the indices closely corresponds to the observed trend of the logarithms of the indices, which was overall bullish before the crashes. The most predicted dates correspond to the start dates of the stock market crashes identified by the CMAX approach. Therefore, the forecasted stock market crashes are the results of the bursting of speculative bubbles and, consequently, of the price deviation from their fundamental values.Practical implicationsThe adoption of the LPPL model might be very beneficial for financial market participants in reducing their financial crash risk exposure and managing their equity portfolio risk.Originality/valueThis study differs from previous research in several ways. First of all, to the best of the authors' knowledge, the authors' paper is among the first to show stock market crises detection and prediction, specifically in African countries, since they generate recessionary economic and social dynamics on a large extent and on multiple regional and global scales. Second, in this manuscript, the authors employ the LPPL model, which can expect the most probable day of the beginning of the crash by analyzing excessive stock price volatility.

Effects of ultrasonic pretreatment and drying approaches on the drying kinetics and rehydration of sprouted mung beans

AbstractSprouting is one of the most traditional methods used to decrease most of the antinutritional elements in legumes. The assistance of ultrasound appears to enhance the drying step of the sprouted legumes. The aim of this study was to examine the influence of ultrasound pretreatment and drying methods (hot‐air and infrared) on the drying time, mass transfer kinetic, effective moisture diffusivity (Deff), and rehydration ratio of sprouted mung beans. The ultrasound process (40 kHz and 150 W) was performed in an ultrasonic bath for 0, 5, 10, 15, and 20 min. The results showed that the ultrasonic pretreatment increased the moisture diffusion capacity (higher moisture loss) and reduced the drying time of sprouted mung beans. Also, the drying time of samples in the infrared dryer was significantly less than that in the hot‐air dryer (p < .05). The Deff determined by Fick's second law was varied from 1.36 × 10−10 to 1.88 × 10−10 m2 s−1, and from 1.18 × 10−9 to 1.85 × 10−9 m2 s−1, for samples dried in hot‐air and infrared dryers, respectively. Comparing the coefficient of determination (r), sum of squared error (SSE), and root mean squared error (RMSE) values of 10 models, it was concluded that the Midilli model represents the drying characteristics of sprouted mung beans better than the others. The rehydration ratio of dried samples in hot‐air and infrared dryers increased when the ultrasound pretreatment time was increased. In general, the use of ultrasound pretreatment (about 20 min) and an infrared dryer is a promising drying technique for sprouted mung beans with higher mass transfer and a shorter drying time.

Comparison of Distance Measurements Based on k-Numbers and Its Influence to Clustering

Heuristic data requires appropriate clustering methods to avoid casting doubt on the information generated by the grouping process. Determining an optimal cluster choice from the results of grouping is still challenging. This study aimed to analyze the four numerical measurement formulas in light of the data patterns from categorical that are now accessible to give users of heuristic data recommendations for how to derive knowledge or information from the best clusters. The method used was clustering with four measurements: Euclidean, Canberra, Manhattan, and Dynamic Time Warping and Elbow approach for optimizing. The Elbow with Sum Square Error (SSE) is employed to calculate the optimal cluster. The number of test clusters ranges from k = 2 to k = 10. Student data from social media was used in testing to help students achieve higher GPAs. 300 completed questionnaires that were circulated and used to collect the data. The result of this study showed that the Manhattan Distance is the best numerical measurement with the largest SSE of 45.359 and optimal clustering at k = 5. The optimal cluster Manhattan generated was made up of students with GPAs above 3.00 and websites/ vlogs used as learning tools by the mathematics and computer department. Each cluster’s ability to create information can be impacted by the proximity of qualities caused by variations in the number of clusters.

On the Distribution of the Product of Inverse Pareto and Exponential Random Variables

This article considers Inverse Pareto and Exponential distributions to create the distribution of the product. The researchers derived its properties, such as; survival functions and hazard functions, and used the model criterion such as Sum Square Error (SSE), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) in estimating the parameters for deriving the best joint distribution between monthly precipitation and temperature in the Philippines from 1974 to 2013. The results showed that considering the monthly precipitation and temperature data, the distribution of the product of Inverse Pareto and Exponential outperformed the other existing distribution of the product.

Exploring the synergistic effects of calcium chloride modification on stem bark eucalyptus biochar for Cr(VI) and Pb(II) ions removal: Kinetics, isotherm, thermodynamic and optimization studies

In this study, stem bark eucalyptus was subjected to pyrolysis modification to produce modified biochar. The modified biochar (MSBEB) was characterized using Fourier Transform Infrared Spectroscopy (FTIR), Scanning electron microscopy coupled with energy-dispersive X-ray spectroscopy (SEM-EDS), X-ray Diffraction (XRD), and Brunauer–Emmett–Teller (BET) techniques. The impact of adsorption process variables such as temperature, adsorbent dosage, pH and contact time on the metals ion removal efficiency were investigated. The optimum conditions for maximum removal of Cr(VI) and Pb(II) ions were determined as 45.20 °C, 0.12 g/L, and 120.5 min through optimization process. The excellent performance of the modified biochar can be attributed to its porous structure, surface area, surface chemistry and crystallinity as supported by SEM, BET, FTIR and XRD analysis. However, based on the high correlation coefficient (R2), low values of chi square (χ2) and sum of square error (SSE), the Freundlich isotherm and Pseudo-second order kinetics provided the best fit, suggesting chemisorption as the dominant mechanism. Thermodynamic analysis indicated an endothermic, spontaneous, and feasible reaction.

Exploiting carboxymethyl cellulose-starch/alumina nano gel to eliminate Fe(III) from ore leachates of rare earth elements

AbstractThe present study describes the development of a novel nano gel of Carboxymethyl Cellulose Starch and Alumina (CMC-St/Al2O3) to purify the leach liquor of rare earth elements (REEs) minerals from Fe(III), which is considered the most contaminating metal in the REE liquor. CMC-St/Al2O3 nano gel was recognized by different analytical techniques such as FT-IR, SEM, TEM, X-ray diffraction, particle size, and thermal analysis. In a batch study, the best conditions for purifying REE from Fe(III) contaminants using CMC-St/Al2O3 nano gel were determined. For an initial concentration of 100 mg L−1, 97.6% of Fe(III) was efficiently adsorbed onto CMC-St/Al2O3 after 15.0 min, pH = 2, and 25 °C. Due to the competition effect, the sorption efficiencies of the binary systems decreased to 68.4%, 72.97%, and 84.71% for the systems Fe(III)/La(III), Fe(III)/Sr(II), and Fe(III)/Cs(I), respectively. 99.9% of Fe(III) is eluted by 0.50 mol L−1 H2SO4. The sorption process was fitted with pseudo-second-order and the Langmuir model based on the error functions: Coefficient of determination (R2), Reduced Chi-square (χ2), The sum of square errors (SSE), and Corrected Akaike Information Criterion (AICc) as well as Residual error plots. The sorption process was spontaneous and exothermic. Finally, a CMC-St/Al2O3 nano gel was used to separate Fe(III) from the monazite liquor minerals and Sela leachate, mineralized from the Rosetta area and Gabal El Sela at Halaib environs, Egypt, with efficiencies of 89.03 and 92.7%, respectively.

An evolutionary multi-algorithm based framework for the parametric estimation of proton exchange membrane fuel cell

This paper proposes a multi-strategy, multiple algorithms based hybrid strategy using flower pollination algorithm (FPA), grey wolf optimizer (GWO), INFO, and naked mole rat algorithm (NMRA). The proposed algorithm, named the Flower Grey INFO Naked (FGIN) algorithm, incorporates the most effective equations from the FPA, GWO, INFO, and NMRA. Here FPA’s basic structure following global and local search is used, GWO is meant for providing extensive exploration, whereas INFO and NMRA both contribute towards exploitative search. Dynamic iterative search and population segmentation strategies are incorporated for enhanced performance of FGIN algorithm. For enhanced self-adaptivity, six mutation weight operators are applied to the three parameters of the proposed strategy. FGIN is also subjected to higher dimensional and variable population analysis, and has been found to be highly effective. A deeper analysis using CEC 2005, CEC 2017, CEC 2019 and CEC 2022 benchmark data set is also performed to validate the superiority of the proposed algorithm with respect to success history based differential evolution (SHADE), self-adaptive DE (SaDE), NL-LSHADE-LBC, DE with active archive (JADE), LSHADE-SPACMA, evolutionary algorithms with eigen crossover (EA4eig), extended GWO (GWO-E), NL-LSHADE-RSP-MID, jDE100, and others. The proposed FIGN algorithm is then used for the parametric identification of proton exchange membranes in fuel cells (PEMFC). The optimization challenge of PEMFC is to minimize the sum of squared error (SSE) between the experimental and measured voltage. And also determine, the optimal values of seven unknown parameters for the PEMFC stack’s. To illustrate the potential of the FGIN algorithm is validated by utilizing five well-known commercial PEMFCs, namely NedStack PS6, BCS 500 W, Stack 250 W, Ballard Mark V, and Horizon H-12 Stack. In order to check the effectiveness of the FGIN algorithm, both parametric and non-parametric statistical tests have been conducted, and it has been found that the proposed algorithm performs significantly better.

Machine Learning-Based Approaches for Credit Card Fraud Detection: A Comprehensive Reviewz

The objective of data analytics is to discover hidden patterns and use them to guide wise judgements in a range of circumstances. Theft of credit cards has significantly grown as a result of modern technologies and has become a popular target for scam artists. Publicly available databases on credit card fraud are very unbalanced. As more people conduct business online, Fraud involving credit cards has grown to be a serious problem for both consumers and financial establishments. standard rule-based fraud detection strategies have shown to be insufficient to combat fraudsters' ever-evolving tactics. Machine learning algorithms have thus developed into a powerful tool for real-time unsupervised learning, and anomaly detection., is then explored in detail in order to accurately identify fraudulent transactions. Furthermore, we explore the various data features utilized by machine learning algorithms, including transaction history, transaction amounts, merchant information, and geographical locations. “For people, companies, and financial institutions, A significant financial danger is credit card fraud. In order to detect theft, robust methods for machine learning must be developed. researchers can help minimize financial losses associated with fraudulent activities”. In this research we will be using weighted product method. Taken as Alternative parameters is “Fraud detection using Game theory for M1, Hybrid Approach For Fraud Detection Using Svm And Decision Tree for M2, Fraud Detection Using Som & Psofor M3, Dempster Shafer Theory Along With Bayesian Learning For Detecting Fraudfor M4, Cardwatchfor M5”. Taken as Evaluation parameters is “Sum of Squared Error, Mean Squared error, Root Mean Square error, Mean Absolute error, Root Mean Square Prediction Error, and Accuracy”. Model 1 outperformed the other 4 models when a machine learning algorithm was used to identify credit card frauds. With Weighted Product Method we are able to find the best way of detection of credit card frauds by machine learning algorithm which has been evaluated with various parameters and methodology.

Study on influencing factors and optimization of carbon fiber wear resistance test

In order to accurately distinguish the wear resistance level of different carbon fibers including high strength fibers and high modulus fibers, and ensure minimal fluctuations in testing results, orthogonal tests are designed based on the testing method of carbon fiber wear resistance from the standard Q/ZHFC 4403-2014, and the influencing factors of wear resistance test is determined, and the corresponding test parameters were optimized by the error sum of squares. The results show that within a certain factor level, the traction tension, friction load, friction rod angle and the number of friction rods have a highly significant impact on the test results of fuzz mass, the traction speed has an impact on the test results, and the density of sponge sheet has no impact. When the traction tension is 25N, the friction load is 350g, the traction speed is 30m/min, and the sponge density is 2.28×10−2g/cm3, the angle of friction rod is 120°, the coefficient of variation of the fuzz mass test results is 2.9%~5.0%, which means the testing method with optimized parameters can accurately and quantitatively distinguish the wear resistance level of different brand carbon fibers.

Encapsulation of açaí (Euterpe oleracea) pulp with whey protein isolate by spray-drying: An optimization study using response surface methodology (RSM)

Açaí fruit (Euterpe oleracea) is a rich source of bioactive compounds such as anthocyanins and flavonoids in general. However, once anthocyanins are easily degradable, efforts have been made toward the development of methods for preserving them from degradation throughout industrial processing. The objective of this study was to optimize the encapsulation of açaí pulp with whey protein isolate by spray drying. For this purpose, the Central Composite Rotational Design (CCRD) with response surface methodology (RSM) was applied to evaluate the influence of inlet temperature (Te), drying air flow rate (VA), and compressed air flow rate (VB) on the following response variables: encapsulation yield, water activity, hygroscopicity, density, ash, and protein, in addition to the content of the bioactive compounds anthocyanins and flavonoids. The coefficient of determination (R²) of CCRD ranged between 0.87 and 0.97, and the sum of squared error (SSE) varied from 0.0003 to 14505, indicating an adequate performance of this experimental design. In general, the optimization analysis showed that Te between 150 and 165 °C, VA below 2.9×10−5 m³ /s and VB less than 0.0006 m³ /s favored the minimization of water activity and hygroscopicity, 0.25 and 2.9 g/100 g, respectively, the maximization of density, and encapsulation yield (around 45%), as well as the preservation of both the anthocyanins (170 mg .100 g−1) and flavonoids (420 mg. 100 g−1), respectively, obtaining a high-quality product. This study represents a first step in the encapsulation of açaí, aiming not only to preserve its bioactive compounds but also to provide a product with a rich protein source, such as whey protein. Ultimately, this research offers potential industrial production alternatives, opens up a new field of study, and presents a potential new market opportunity for small, medium, and even large-scale producers.

Modeling the Effect of Temperature on Ethanol Fermentation Using Saccharomyces Cerevisiae CSI-1 by Genetic Programming

In this study, genetic programming (GP) was the systematic method used to identify the structure and parameters of a mathematical model for ethanol fermentation. The mathematical model simulated the effect of temperature on the kinetics of batch ethanol fermentation and helped to find out the optimum temperature for the better performance of the process. Saccharomyces cerevisiae CSI-1 growing in cane molasses-based media was the microorganism used in all the experiments. Achieving the model’s precision in describing the experimental observations involved the estimation of its structure (non-linear principally) and its constant parameters. The model found describes the fermentation kinetics and showed a fair prediction for Dry cell weight (DCW), Colony forming units/mL (CFU/mL), Residual sucrose (RS), Residual glucose (RG) and Ethanol concentration (E). The model was used to optimize the operating conditions of the process. The predictions from the model in terms of Mean Square Error (MSE) and Sum Squared Error (SSE) fitted the experimental data well with fitness values in a range of R2 ? 0:92.

Influence of PPD and Mass Scaling Parameter on the Goodness of Fit of Dry Ice Compaction Curve Obtained in Numerical Simulations Utilizing Smoothed Particle Method (SPH) for Improving the Energy Efficiency of Dry Ice Compaction Process

The urgent need to reduce industrial electricity consumption due to diminishing fossil fuels and environmental concerns drives the pursuit of energy-efficient production processes. This study addresses this challenge by investigating the Smoothed Particle Method (SPH) for simulating dry ice compaction, an intricate process poorly addressed by conventional methods. The Finite Element Method (FEM) and SPH have been dealt with by researchers, yet a gap persists regarding SPH mesh parameters’ influence on the empirical curve fit. This research systematically explores Particle Packing Density (PPD) and Mass Scaling (MS) effects on the agreement between simulation and experimental outputs. The Sum of Squared Errors (SSE) method was used for this assessment. By comparing the obtained FEM and SPH results under diverse PPD and MS settings, this study sheds light on the SPH method’s potential in optimizing the dry ice compaction process’s efficiency. The SSE based analyses showed that the goodness of fit did not vary considerably for PDD values of 4 and up. In the case of MS, a better fit was obtained for its lower values. In turn, for the ultimate compression force FC, an empirical curve fit was obtained for PDD values of 4 and up. That said, the value of MS had no significant bearing on the ultimate compression force FC. The insights gleaned from this research can largely improve the existing sustainability practices and process design in various energy-conscious industries.

The Optimization of a Pipeline Temperature Monitoring Method Based on Non-Local Means with the Black Widow Optimization Algorithm

The accuracy of pipeline temperature monitoring using the Brillouin Optical Time Domain Analysis system depends on the Brillouin Gain Spectrum in the Brillouin Optical Time Domain Analysis system. The Non-Local Means noise reduction algorithm, due to its ability to use the data patterns available within the two-dimensional measurement data space, has been used to improve the Brillouin Gain Spectrum in the Brillouin Optical Time Domain Analysis system. This paper studies a new Non-Local Means algorithm optimized through the Black Widow Optimization Algorithm, in view of the unreasonable selection of smoothing parameters in other Non-Local Means algorithms. The field test demonstrates that, the new algorithm, when compared to other Non-Local Means methods, excels in preserving the detailed information within the Brillouin Gain Spectrum. It successfully restores the fundamental shape and essential characteristics of the Brillouin Gain Spectrum. Notably, at the 25 km fiber end, it achieves a 3 dB higher Signal-to-Noise Ratio compared to other Non-Local Means noise reduction algorithms. Furthermore, the Brillouin Gain Spectrum values exhibit increases of 9.4% in Root Mean Square Error, 12.5% in Sum of Squares Error, and 10% in Full Width at Half Maximum. The improved method has a better denoising effect and broad application prospects in pipeline safety.

A customized deep learning-based framework for classification and analysis of social media posts to enhance the Hajj and Umrah services

Each year, millions of pilgrims come to Saudi Arabia to perform Hajj and Umrah. To help pilgrims with their difficulties and make plans to enhance the Hajj and Umrah services, this article offers a deep learning-based framework to categorize and analyze pilgrims’ posts on social media networks X (formerly Twitter), Facebook and Instagram. We extracted Arabic posts related to Hajj/Umrah then tokenized and pre-processed the dataset to remove unnecessary parts such as punctuation. Posts are manually labeled into five classes: Health, Organization, Security, Services, and Worship. Labeled posts are collected to build a Long Short-Term Memory (LSTM) network classifier for deep learning. To increase the prediction accuracy, we customized the LSTM classification layer and used the sum of squares error (SSE) loss function instead of the default cross-entropy loss function. A rigorous simulation is run to assess the system’s effectiveness. Every time a simulation round occurs, the trained network is tasked with identifying the classes of unlabeled posts (testing data). Similar tests are performed using the K-Nearest Neighbors (KNN) and Linear Discriminant Analysis (LDA) algorithms for comparative analysis. Accuracy, confusion matrix, precision, sensitivity, specificity, and F1 score are used to quantify the system performance. The maximum mean accuracy of the proposed framework, KNN and LDA are 85.65%, 68.47%, and 59.06% respectively. The proposed framework needs to be integrated into a larger system called the Intelligent Pilgrim Service System (IPSS). We described the IPSS architecture, which comprises modules for data generation, data storage (on the cloud), and a control center. We described a hashtag mechanism as a part of the IPSS. This hashtag mechanism will provide both general and focused advice to millions of pilgrims related to their social media posts. We discussed scenarios of how the IPSS can enhance the Hajj and Umrah services.

Distributed Muskingum model with a Whale Optimization Algorithm for river flood routing

Abstract This research introduces a novel nonlinear Muskingum model for river flood routing, aiming to enhance accuracy in modeling. It integrates lateral inflows using the Whale Optimization Algorithm (WOA) and employs a distributed Muskingum model, dividing river reaches into smaller intervals for precise calculations. The primary goal is to minimize the Sum of Square Errors (SSE) between the observed and modeled outflows. Our methodology is applied to six distinct flood hydrographs, revealing its versatility and efficacy. For Lawler's and Dinavar's flood data, the single-reach Muskingum model outperforms multi-reach versions, demonstrating its effectiveness in handling lateral inflows. For Lawler's data, the single-reach model (NR = 1) yields optimal parameters of K = 0.392, x = 0.027, m = 1.511, and β = 0.010, delivering superior results. Conversely, when fitting flood data from Wilson, Wye, Linsley, and Viessman and Lewis, the multi-reach Muskingum model exhibits better overall performance. Remarkably, the model excels with the Viessman and Lewis flood data, especially with two reaches (NR = 2), achieving a 21.6% SSE improvement while employing the same parameter set. This research represents a significant advancement in flood modeling, offering heightened accuracy and adaptability in river flood routing.

Heuristic-Based Algorithms for Low-Complexity AV1 Intraprediction

Modern video encoders, such as the state-of-the-art AOMedia Video 1 (AV1) and Versatile Video Coding (VVC), offer significant compression gains at the cost of an increase in computational effort. This is partially because of the novel intra prediction techniques, including an increased number of prediction modes and block sizes supported by the codecs. To reduce this computational effort, this work proposes two heuristic-based algorithms for AV1 intra prediction: a fast mode decision that reduces the number of intra candidates with a low-cost direction detection method, and a mode-adaptive subsampling algorithm that significantly reduces the number of Sum of Squared Errors (SSE) operations after prediction. On average, a notable encoding time reduction of 29.8% was achieved, at the cost of a compression efficiency loss of 1.28%.

Applicability of the equilibrium adsorption isotherms and the statistical tools on to them: a case study for the adsorption of fluoride onto Mg-Fe-CO3 LDH

The demand for a low-cost, easy-to-use, low-maintenance system of adsorbents for detoxifying wastewater effluents is growing. A proper understanding of adsorption mechanisms, their controls, and adsorbate-adsorbent behavior is essential. Thus, the current study deals with the required understanding of linear equilibrium adsorption isotherm models. The adsorption data of different concentrations of fluoride onto Mg-Fe-CO3 LDH is fitted to isotherm models. The two-parameter models discussed are Langmuir, Freundlich, Temkin, and Dubinin-Radushkevich, whereas the three-parameter model cited is Redlich-Peterson. To identify the best-fitting model(s) in an equilibrium isotherm study to quantitatively represent the relevant sorption system, various error functions and statistical tools, such as average relative error deviation (ARED), sum of square errors (ERRSQ or SSE), hybrid relative error function (HYBRID), Marquardt’s percent standard error deviation (MPSD), sum of absolute errors (EABS), sum of normalized errors (SNE), correlation coefficient of Pearson (r), coefficient of determination (r2), chi-square test (χ2), student’s T-test and F-test were applied. It is found that the Temkin model best fits the isotherm data, and the sorption process occurs over multiple layers as per the Freundlich isotherm and was found to be more promising than Langmuir’s monolayer sorption process. The exothermic physisorption course for the adsorbate-absorbent interactions is deduced from the isotherm parameters.

A Microwave Radiometer Residual Inversion Neural Network Based on a Deadband Conditioning Model

Microwave radiometers are passive remote sensing devices that are widely used in marine atmospheric observations. The accuracy of its inversion of temperature and humidity profiles is an important indicator of its performance. Back Propagation (BP) neural networks are widely used in the study of microwave radiometer inversion problems. However, the BP network which is carried by the radiometer inversion suffers from profile data collapse. To address this, this study introduced a residual network to improve the accuracy of water vapor vertical profiles. Aiming at the problem of large inversion temperature error due to the effect of turbulence on the light-travel phase induced by stationary fronts along the seashore in the subtropical monsoon climate region, we used historical data to establish the seasonal a priori mean profile and design a dead-zone residual adjustment model. The accuracy of the residual network and the deadband-adjusted residual network was verified using the meteorological records of the Taizhou region from 2013–2018, with the experimental data and BP hierarchical network as the comparison term. We found no data collapse in the temperature and humidity profile inversion results of the residual network. Relative to the initial BP hierarchical algorithm, where the error of water vapor in the range 6–10 km was reduced by 80%, the dead zone residual adjustment model in the inverse-temperature phenomenon reduced the sum of squares error by 21%, compared with the ordinary residual network inversion results. Our findings provide new insights into the accuracy improvement of radiometer remote sensing.

DEVELOPMENT OF SEAMED COMPRESSION SOCKS AND COMPARISON WITH CLASS I SOCKS USING EXISTING MATHEMATICAL MODELS

Compression therapy is an important method for treating venous diseases such as venous edema and venous hypertension. Regular compression therapy's main objective is to diminish leg swelling by controlling blood flow and avoiding the recurrence of reversible blood flow. Compression socks are often recommended as therapeutic garments. In this study, a seamed compression sock was developed using fabric with an interlock knit structure. Three other sock samples were produced by using circular knitting MERZ CC4 model machine for comparison. The results demonstrate that the developed sock meets all the requirements of compression class I. Statistical analysis reveals that fabric parameters, particularly fabric weight, effectively explain compression pressure intensity according to the values of coefficient of determination, coefficient of correlation (r), and means sum of square errors (MSE). In this work, Laplace's Law and a few preexisting mathematical models were used to calculate the compression pressure of both standard compression socks and socks with seams, with results that were essentially similar. The points of data are tightly clustered around line of regression, showing that there is little variation in the compression pressure for socks with seams.

Deep learning model based on Bayesian optimization for predicting the infinite dilution activity coefficients of ionic liquid-solute systems

The infinite dilution activity coefficient (γ∞) is a crucial thermodynamic property that provides a measure of the affinity between the solute and the solvent. In this work, three deep learning models (deep neural network, convolution neural network, and convolution deep neural network) were proposed to predict the γ∞ for ionic liquid-solute systems. 52 ionic liquids and 114 organic solutes (7783 data points in total) contained in the γ∞ database over the temperature from 293.15 to 428.15 K were collected to construct the model. Molecular descriptor was generated using the RDKit. The Bayesian optimization algorithm was employed to determine the parameters for each model, and the stability of the model was increased by 10-fold cross validation. Finally, the method of SHapley Additive exPlanations was employed to explain our proposed model. The coefficient of determination, mean absolute error, mean square error, root mean square error, error, sum of squared error, relative root mean square error and the Wilcoxon signed-rank test were used to assess the model. The results indicated that the experimental values were in satisfactory agreement with the values predicted for convolution deep neural network. These predictive models can be used to predict the γ∞ for ionic liquid-solute systems to solve problems in phase equilibrium and process design.