On fractional discrete financial system:Bifurcation,chaos,and control

The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets.This paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders.As such,we evaluate when the equilibrium points are stable or unstable at various fractional orders.We use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov exponent.These techniques reveal that financial maps exhibit chaotic attractor behavior.This study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate orders.Furthermore,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm.Additionally,we offer nonlinear-type controllers to stabilize the fractional financial map.The numerical results of this study are obtained using MATLAB.

Composite Fractional Trapezoidal Rule with Romberg Integration

The aim of this research is to demonstrate a novel scheme for approximating the Riemann-Liouville fractional integral operator.This would be achieved by first establishing a fractional-order version of the 2-point Trapezoidal rule and then by proposing another fractional-order version of the(n+1)-composite Trapezoidal rule.In particular,the so-called divided-difference formula is typically employed to derive the 2-point Trapezoidal rule,which has accordingly been used to derive a more accurate fractional-order formula called the(n+1)-composite Trapezoidal rule.Additionally,in order to increase the accuracy of the proposed approximations by reducing the true errors,we incorporate the so-called Romberg integration,which is an extrapolation formula of the Trapezoidal rule for integration,into our proposed approaches.Several numerical examples are provided and compared with a modern definition of the Riemann-Liouville fractional integral operator to illustrate the efficacy of our scheme.

An Efficient ResNetSE Architecture for Smoking Activity Recognition from Smartwatch

Smoking is a major cause of cancer,heart disease and other afflictions that lead to early mortality.An effective smoking classification mechanism that provides insights into individual smoking habits would assist in implementing addiction treatment initiatives.Smoking activities often accompany other activities such as drinking or eating.Consequently,smoking activity recognition can be a challenging topic in human activity recognition(HAR).A deep learning framework for smoking activity recognition(SAR)employing smartwatch sensors was proposed together with a deep residual network combined with squeeze-and-excitation modules(ResNetSE)to increase the effectiveness of the SAR framework.The proposed model was tested against basic convolutional neural networks(CNNs)and recurrent neural networks(LSTM,BiLSTM,GRU and BiGRU)to recognize smoking and other similar activities such as drinking,eating and walking using the UT-Smoke dataset.Three different scenarios were investigated for their recognition performances using standard HAR metrics(accuracy,F1-score and the area under the ROC curve).Our proposed ResNetSE outperformed the other basic deep learning networks,with maximum accuracy of 98.63%.

Automatic Recognition of Construction Worker Activities Using Deep Learning Approaches and Wearable Inertial Sensors

The automated evaluation and analysis of employee behavior in an Industry 4.0-compliant manufacturingfirm are vital for the rapid and accurate diagnosis of work performance,particularly during the training of a new worker.Various techniques for identifying and detecting worker performance in industrial applications are based on computer vision techniques.Despite widespread com-puter vision-based approaches,it is challenging to develop technologies that assist the automated monitoring of worker actions at external working sites where cam-era deployment is problematic.Through the use of wearable inertial sensors,we propose a deep learning method for automatically recognizing the activities of construction workers.The suggested method incorporates a convolutional neural network,residual connection blocks,and multi-branch aggregate transformation modules for high-performance recognition of complicated activities such as con-struction worker tasks.The proposed approach has been evaluated using standard performance measures,such as precision,F1-score,and AUC,using a publicly available benchmark dataset known as VTT-ConIoT,which contains genuine con-struction work activities.In addition,standard deep learning models(CNNs,RNNs,and hybrid models)were developed in different empirical circumstances to compare them to the proposed model.With an average accuracy of 99.71%and an average F1-score of 99.71%,the experimentalfindings revealed that the suggested model could accurately recognize the actions of construction workers.Furthermore,we examined the impact of window size and sensor position on the identification efficiency of the proposed method.

Deep Pyramidal Residual Network for Indoor-Outdoor Activity Recognition Based on Wearable Sensor

Recognition of human activity is one of the most exciting aspects of time-series classification,with substantial practical and theoretical impli-cations.Recent evidence indicates that activity recognition from wearable sensors is an effective technique for tracking elderly adults and children in indoor and outdoor environments.Consequently,researchers have demon-strated considerable passion for developing cutting-edge deep learning sys-tems capable of exploiting unprocessed sensor data from wearable devices and generating practical decision assistance in many contexts.This study provides a deep learning-based approach for recognizing indoor and outdoor movement utilizing an enhanced deep pyramidal residual model called Sen-PyramidNet and motion information from wearable sensors(accelerometer and gyroscope).The suggested technique develops a residual unit based on a deep pyramidal residual network and introduces the concept of a pyramidal residual unit to increase detection capability.The proposed deep learning-based model was assessed using the publicly available 19Nonsens dataset,which gathered motion signals from various indoor and outdoor activities,including practicing various body parts.The experimental findings demon-strate that the proposed approach can efficiently reuse characteristics and has achieved an identification accuracy of 96.37%for indoor and 97.25%for outdoor activity.Moreover,comparison experiments demonstrate that the SenPyramidNet surpasses other cutting-edge deep learning models in terms of accuracy and F1-score.Furthermore,this study explores the influence of several wearable sensors on indoor and outdoor action recognition ability.

A Comprehensive Evaluation of State-of-the-Art Deep Learning Models for Road Surface Type Classification

In recent years,as intelligent transportation systems(ITS)such as autonomous driving and advanced driver-assistance systems have become more popular,there has been a rise in the need for different sources of traffic situation data.The classification of the road surface type,also known as the RST,is among the most essential of these situational data and can be utilized across the entirety of the ITS domain.Recently,the benefits of deep learning(DL)approaches for sensor-based RST classification have been demonstrated by automatic feature extraction without manual methods.The ability to extract important features is vital in making RST classification more accurate.This work investigates the most recent advances in DL algorithms for sensor-based RST classification and explores appropriate feature extraction models.We used different convolutional neural networks to understand the functional architecture better;we constructed an enhanced DL model called SE-ResNet,which uses residual connections and squeeze-and-excitation mod-ules to improve the classification performance.Comparative experiments with a publicly available benchmark dataset,the passive vehicular sensors dataset,have shown that SE-ResNet outperforms other state-of-the-art models.The proposed model achieved the highest accuracy of 98.41%and the highest F1-score of 98.19%when classifying surfaces into segments of dirt,cobblestone,or asphalt roads.Moreover,the proposed model significantly outperforms DL networks(CNN,LSTM,and CNN-LSTM).The proposed RE-ResNet achieved the classification accuracies of asphalt roads at 98.98,cobblestone roads at 97.02,and dirt roads at 99.56%,respectively.

Pre-Impact and Impact Fall Detection Based on a Multimodal Sensor Using a Deep Residual Network

Falls are the contributing factor to both fatal and nonfatal injuries in the elderly.Therefore,pre-impact fall detection,which identifies a fall before the body collides with the floor,would be essential.Recently,researchers have turned their attention from post-impact fall detection to pre-impact fall detection.Pre-impact fall detection solutions typically use either a threshold-based or machine learning-based approach,although the threshold value would be difficult to accu-rately determine in threshold-based methods.Moreover,while additional features could sometimes assist in categorizing falls and non-falls more precisely,the esti-mated determination of the significant features would be too time-intensive,thus using a significant portion of the algorithm’s operating time.In this work,we developed a deep residual network with aggregation transformation called FDSNeXt for a pre-impact fall detection approach employing wearable inertial sensors.The proposed network was introduced to address the limitations of fea-ture extraction,threshold definition,and algorithm complexity.After training on a large-scale motion dataset,the KFall dataset,and straightforward evaluation with standard metrics,the proposed approach identified pre-impact and impact falls with high accuracy of 91.87 and 92.52%,respectively.In addition,we have inves-tigated fall detection’s performances of three state-of-the-art deep learning models such as a convolutional neural network(CNN),a long short-term memory neural network(LSTM),and a hybrid model(CNN-LSTM).The experimental results showed that the proposed FDSNeXt model outperformed these deep learning models(CNN,LSTM,and CNN-LSTM)with significant improvements.

Driving Activity Classification Using Deep Residual Networks Based on Smart Glasses Sensors

Accidents are still an issue in an intelligent transportation system,despite developments in self-driving technology(ITS).Drivers who engage in risky behavior account for more than half of all road accidents.As a result,reckless driving behaviour can cause congestion and delays.Computer vision and multimodal sensors have been used to study driving behaviour categorization to lessen this problem.Previous research has also collected and analyzed a wide range of data,including electroencephalography(EEG),electrooculography(EOG),and photographs of the driver’s face.On the other hand,driving a car is a complicated action that requires a wide range of body move-ments.In this work,we proposed a ResNet-SE model,an efficient deep learning classifier for driving activity clas-sification based on signal data obtained in real-world traffic conditions using smart glasses.End-to-end learning can be achieved by combining residual networks and channel attention approaches into a single learning model.Sensor data from 3-point EOG electrodes,tri-axial accelerometer,and tri-axial gyroscope from the Smart Glasses dataset was utilized in this study.We performed various experiments and compared the proposed model to base-line deep learning algorithms(CNNs and LSTMs)to demonstrate its performance.According to the research results,the proposed model outperforms the previous deep learning models in this domain with an accuracy of 99.17%and an F1-score of 98.96%.

Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking

This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers.

A NONLOCAL HYBRID BOUNDARY VALUE PROBLEM OF CAPUTO FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

In this paper, we discuss the existence of solutions for a nonlocal hybrid boundary value problem of Caputo fractional integro-differential equations. Our main result is based on a hybrid fixed point theorem for a sum of three operators due to Dhage, and is well illustrated with the aid of an example.

A New Medical Image Enhancement Algorithm Based on Fractional Calculus

The enhancement of medical images is a challenging research task due to the unforeseeable variation in the quality of the captured images.The captured images may present with low contrast and low visibility,which might inuence the accuracy of the diagnosis process.To overcome this problem,this paper presents a new fractional integral entropy(FITE)that estimates the unforeseeable probabilities of image pixels,posing as the main contribution of the paper.The proposed model dynamically enhances the image based on the image contents.The main advantage of FITE lies in its capability to enhance the low contrast intensities through pixels’probability.Initially,the pixel probability of the fractional power is utilized to extract the illumination value from the pixels of the image.Next,the contrast of the image is then adjusted to enhance the regions with low visibility.Finally,the fractional integral entropy approach is implemented to enhance the low visibility contents from the input image.Tests were conducted on brain MRI,lungs CT,and kidney MRI scans datasets of different image qualities to show that the proposed model is robust and can withstand dramatic variations in quality.The obtained comparative results show that the proposed image enhancement model achieves the best BRISQUE and NIQE scores.Overall,this model improves the details of brain MRI,lungs CT,and kidney MRI scans,and could therefore potentially help the medical staff during the diagnosis process.

Attractive Multistep Reproducing Kernel Approach for Solving Stiffness Differential Systems of Ordinary Differential Equations and Some Error Analysis

In this paper,an efficient multi-step scheme is presented based on reproducing kernel Hilbert space(RKHS)theory for solving ordinary stiff differential systems.The solution methodology depends on reproducing kernel functions to obtain analytic solutions in a uniform formfor a rapidly convergent series in the posed Sobolev space.Using the Gram-Schmidt orthogonality process,complete orthogonal essential functions are obtained in a compact field to encompass Fourier series expansion with the help of kernel properties reproduction.Consequently,by applying the standard RKHS method to each subinterval,approximate solutions that converge uniformly to the exact solutions are obtained.For this purpose,several numerical examples are tested to show proposed algorithm’s superiority,simplicity,and efficiency.The gained results indicate that themulti-step RKHSmethod is suitable for solving linear and nonlinear stiffness systems over an extensive duration and giving highly accurate outcomes.

Thermogram Adaptive Efficient Model for Breast Cancer Detection Using Fractional Derivative Mask and Hybrid Feature Set in the IoT Environment

In this paper,a novel hybrid texture feature set and fractional derivative filter-based breast cancer detection model is introduced.This paper also introduces the application of a histogram of linear bipolar pattern features(HLBP)for breast thermogram classification.Initially,breast tissues are separated by masking operation and filtered by Gr¨umwald–Letnikov fractional derivative-based Sobel mask to enhance the texture and rectify the noise.A novel hybrid feature set usingHLBP and other statistical feature sets is derived and reduced by principal component analysis.Radial basis function kernel-based support vector machine is employed for detecting the abnormality in the thermogram.The performance parameters are calculated using five-fold cross-validation scheme using MATLAB 2015a simulation software.The proposedmodel achieves the classification accuracy,sensitivity,specificity,and area under the curve of 94.44%,95.55%,92.22%,96.11%,respectively.A comparative investigation of different texture features with respect to fractional orderαto classify the breast malignancy is also presented.The proposed model is also compared with a few existing state-of-art schemes which verifies the efficacy of the model.Fractional orderαoffers extra adaptability in overcoming the limitations of thermal imaging techniques and assists radiologists in prior breast cancer detection.The proposed model is more generalized which can be used with different thermal image acquisition protocols and IoT based applications.

Lie symmetry analysis,explicit solutions,and conservation laws of the time-fractional Fisher equation in two-dimensional space

In these analyses,we consider the time-fractional Fisher equation in two-dimensional space.Through the use of the Riemann-Liouville derivative approach,the well-known Lie point symmetries of the utilized equation are derived.Herein,we overturn the fractional fisher model to a fractional differential equation of nonlinear type by considering its Lie point symmetries.The diminutive equation’s derivative is in the Erdélyi-Kober sense,whilst we use the technique of the power series to conclude explicit solutions for the diminutive equations for the first time.The conservation laws for the dominant equation are built using a novel conservation theorem.Several graphical countenances were utilized to award a visual performance of the obtained solutions.Finally,some concluding remarks and future recommendations are utilized.