Search results for: Lyapunov function

Authors: X. Wang, T. J. Craft, H. Iacovides

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When handling the near-wall regions of turbulent flows, it is necessary to account for the viscous effects which are important over the thin near-wall layers. Low-Reynolds- number turbulence models do this by including explicit viscous and also damping terms which become active in the near-wall regions, and using very fine near-wall grids to properly resolve the steep gradients present. In order to overcome the cost associated with the low-Re turbulence models, a more advanced wall function approach has been implemented within OpenFoam and tested together with a standard log-law based wall function in the prediction of flows which involve 2-D shock wave/turbulent boundary layer interactions (SWTBLIs). On the whole, from the calculation of the impinging shock interaction, the three turbulence modelling strategies, the Lauder-Sharma k-ε model with Yap correction (LS), the high-Re k-ε model with standard wall function (SWF) and analytical wall function (AWF), display good predictions of wall-pressure. However, the SWF approach tends to underestimate the tendency of the flow to separate as a result of the SWTBLI. The analytical wall function, on the other hand, is able to reproduce the shock-induced flow separation and returns predictions similar to those of the low-Re model, using a much coarser mesh.

Keywords: SWTBLIs, skin-friction, turbulence modeling, wall function

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Authors: Takashi Mitsuishi, Koji Saigusa

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This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. The proposed methods are applied to the simple color construct system.

Keywords: periodic membership function, polar coordinates transformation, defuzzification, circular coordinates

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Authors: Hani Albogami

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The internal audit function is considered as one of the internal corporate governance mechanisms that may have an impact on improving earnings quality by constraining earnings management. The internal audit function is also a unique corporate governance mechanism because internal auditors have more involvement with the day-to-day operations comparing to the audit committee, and also internal auditors audit their companies the whole year compared to the external auditor who audits only a certain time of the year. The relationships between internal audit function and earnings management can be understood by some theories. Therefore, this paper provides a theoretical background of the influence of the quality of internal audit function on earnings management. In particular, the agency theory, institutional theory, singling theory, and resource dependency theory are adapted by this paper to provide some understanding and analyses that can be a basis for future research to contribute to the corporate governance academic studies.

Keywords: internal audit, corporate governance, earnings management, accounting

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Authors: Khandoker Akib Mohammad

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While analyzing time-to-event data, it is possible that a certain fraction of subjects will never experience the event of interest, and they are said to be cured. When this feature of survival models is taken into account, the models are commonly referred to as cure models. In the presence of covariates, the conditional survival function of the population can be modelled by using the cure model, which depends on the probability of being uncured (incidence) and the conditional survival function of the uncured subjects (latency), and a combination of logistic regression and Cox proportional hazards (PH) regression is used to model the incidence and latency respectively. In this paper, we have shown the asymptotic normality of the profile likelihood estimator via asymptotic expansion of the profile likelihood and obtain the explicit form of the variance estimator with an implicit function in the profile likelihood. We have also shown the efficient score function based on projection theory and the profile likelihood score function are equal. Our contribution in this paper is that we have expressed the efficient information matrix as the variance of the profile likelihood score function. A simulation study suggests that the estimated standard errors from bootstrap samples (SMCURE package) and the profile likelihood score function (our approach) are providing similar and comparable results. The numerical result of our proposed method is also shown by using the melanoma data from SMCURE R-package, and we compare the results with the output obtained from the SMCURE package.

Keywords: Cox PH model, cure model, efficient score function, EM algorithm, implicit function, profile likelihood

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Authors: Sheng-Fen Fan, Sung-Hui Tseng

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Attention deficit hyperactivity deficit (ADHD) child display diverse sensory processing difficulty behaviors. There is less evidence to figure out how the association between executive function and sensory deficit. To determine whether sensory deficit influence the executive functions, we examined sensory processing by SPM and try to indicate hot/cold executive function (EF) by BRIEF2, respectively. We found that the hot executive function deficit might associate with auditory processing in a variety of settings, and vestibular input to maintain balance and upright posture; the cold EF deficit might opposite to the hot EF deficit, the vestibular sensory modulation difficulty association with emotion shifting and emotional regulation. These results suggest that sensory processing might be another consideration factor to influence the higher cognitive control or emotional regulation of EF. Overall, this study indicates the distinction between hot and cold EF impairments with different sensory modulation problem. Moreover, for clinician, it needs more cautious consideration to conduct intervention with ADHD.

Keywords: hot executive function, cold executive function, sensory processing, ADHD

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Authors: M. R. Al-Rashidi, K. M. El-Naggar, M. F. Al-Hajri

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The fuel cost function describes the electric power generation-cost relationship in thermal plants, hence, it sheds light on economical aspects of power industry. Different models have been proposed to describe this relationship with the quadratic function model being the most popular one. Parameters of second order fuel cost function are estimated in this paper using cuckoo search algorithm. It is a new population based meta-heuristic optimization technique that has been used in this study primarily as an accurate estimation tool. Its main features are flexibility, simplicity, and effectiveness when compared to other estimation techniques. The parameter estimation problem is formulated as an optimization one with the goal being minimizing the error associated with the estimated parameters. A case study is considered in this paper to illustrate cuckoo search promising potential as a valuable estimation and optimization technique.

Keywords: cuckoo search, parameters estimation, fuel cost function, economic dispatch

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Authors: Sule Sahin, Basak Bulut Karageyik

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This paper introduces a hazard rate function for the time of ruin to calculate the conditional probability of ruin for very small intervals. We call this function the force of ruin (FoR). We obtain the expected time of ruin and conditional expected time of ruin from the exact finite time ruin probability with exponential claim amounts. Then we introduce the FoR which gives the conditional probability of ruin and the condition is that ruin has not occurred at time t. We analyse the behavior of the FoR function for different initial surpluses over a specific time interval. We also obtain FoR under the excess of loss reinsurance arrangement and examine the effect of reinsurance on the FoR.

Keywords: conditional time of ruin, finite time ruin probability, force of ruin, reinsurance

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Authors: Madina Hamiane

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Modelling and simulation of an analogy function generator is presented based on a polynomial expansion model. The proposed function generator model is based on a 10th order polynomial approximation of any of the required functions. The polynomial approximations of these functions can then be implemented using basic CMOS circuit blocks. In this paper, a circuit model is proposed that can simultaneously generate many different mathematical functions. The circuit model is designed and simulated with HSPICE and its performance is demonstrated through the simulation of a number of non-linear functions.

Keywords: modelling and simulation, analog function generator, polynomial approximation, CMOS transistors

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Authors: Mohamed Z. M. Duwahir, Shian Gao

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The main objective of this project was to introduce and test a new scheme for parameterization of subsonic aerofoil, using a function called Shape Function. Python programming was used to create a user interactive environment for geometry generation of aerofoil using NACA and Shape Function methodologies. Two aerofoils, NACA 0012 and NACA 1412, were generated using this function. Testing the accuracy of the Shape Function scheme was done by Linear Square Fitting using Python and CFD modelling the aerofoil in Fluent. NACA 0012 (symmetrical aerofoil) was better approximated using Shape Function than NACA 1412 (cambered aerofoil). The second part of the project involved comparing two turbulent models, k-ε and Spalart-Allmaras (SA), in Fluent by modelling the aerofoils NACA 0012 and NACA 1412 in conditions of Reynolds number of 3 × 106. It was shown that SA modelling is better for aerodynamic purpose. The experimental coefficient of lift (Cl) and coefficient of drag (Cd) were compared with empirical wind tunnel data for a range of angle of attack (AOA). As a further step, this project involved drawing and meshing 3D wings in Gambit. The 3D wing flow was solved and compared with 2D aerofoil section experimental results and wind tunnel data.

Keywords: CFD simulation, shape function, turbulent modelling, aerofoil

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Authors: Mohammed Qasim, Kyoung-Dae Kim

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In this paper, we present the design of the super-ellipsoidal potential function (SEPF), that can be used for autonomous collision avoidance of an unmanned aerial vehicle (UAV) in a 3-dimensional space. In the design of SEPF, we have the full control over the shape and size of the potential function. In particular, we can adjust the length, width, height, and the amount of flattening at the tips of the potential function so that the collision avoidance motion vector generated from the potential function can be adjusted accordingly. Based on the idea of the SEPF, we also propose an approach for the local autonomy of a UAV for its collision avoidance when the UAV is teleoperated by a human operator. In our proposed approach, a teleoperated UAV can not only avoid collision autonomously with other surrounding objects but also track the operator’s control input as closely as possible. As a result, an operator can always be in control of the UAV for his/her high-level guidance and navigation task without worrying too much about the UAVs collision avoidance while it is being teleoperated. The effectiveness of the proposed approach is demonstrated through a human-in-the-loop simulation of quadrotor UAV teleoperation using virtual robot experimentation platform (v-rep) and Matlab programs.

Keywords: artificial potential function, autonomous collision avoidance, teleoperation, quadrotor

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Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim

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Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended Kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore, the number of centers will be considered since it affects the performance of approximation.

Keywords: extended Kalman filter, classification problem, radial basis function networks (RBFN), finite impulse response (FIR) filter

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Authors: Negar Miri-Lavasani

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Background: Children with Attention-deficit/hyperactivity disorder (ADHD) show fine motor skills difficulties, and it is controversial whether this difficulty is based on problems in their fine motor skills or their executive function impairments. Objectives of Study: The Fine Motor and Executive Function assessment tool (FiM&EF) was developed to answer the question, ‘Do the fine motor skill deficits in children with ADHD come from their fine motor problems or is it caused by their executive function problems?’. This paper describes the development of a new assessment of Fine Motor and Executive Function (FiM &EF) needed by primary school students with ADHD aged 6-12 years with ADHD. Methods: A study on the content validity established through a survey of a panel of nine experts is explained in detail. Findings: Most the experts agreed such an assessment was needed and two items were deleted as a result of experts’ feedback. Relevance to Clinical Practice: Distinguishing the main reason of fine motor problem in these children could help the clinician for their therapy plans. Knowledge on the influence of executive functioning on fine motor ability in selected age children with ADHD would provide a clearer clinical picture of the fine motor capabilities and executive function for these children.

Keywords: children with ADHD, executive function, fine motor, test

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Authors: Zhe Xu, Jian Li, Lvping Li, Zezheng Dong

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This work is to study an optimized transfer strategy of connecting Earth and Mars via the vicinity of libration points, which have been playing an increasingly important role in trajectory designing on a deep space mission, and can be used as an effective alternative solution for Earth-Mars direct transfer mission in some unusual cases. The use of vicinity of libration points of the sun-planet body system is becoming potential gateways for future interplanetary transfer missions. By adding fuel to cargo spaceships located in spaceports, the interplanetary round-trip exploration shuttle mission of such a system facility can also be a reusable transportation system. In addition, in some cases, when the S/C cruising through invariant manifolds, it can also save a large amount of fuel. Therefore, it is necessary to make an effort on looking for efficient transfer strategies using variant manifold about libration points. It was found that Earth L1/L2 Halo/Lyapunov orbits and Mars L2/L1 Halo/Lyapunov orbits could be connected with reasonable fuel consumption and flight duration with appropriate design. In the paper, the halo hopping method and coplanar circular method are briefly introduced. The former used differential corrections to systematically generate low ΔV transfer trajectories between interplanetary manifolds, while the latter discussed escape and capture trajectories to and from Halo orbits by using impulsive maneuvers at periapsis of the manifolds about libration points. In the following, designs of transfer strategies of the two methods are shown here. A comparative performance analysis of interplanetary transfer strategies of the two methods is carried out accordingly. Comparison of strategies is based on two main criteria: the total fuel consumption required to perform the transfer and the time of flight, as mentioned above. The numeric results showed that the coplanar circular method procedure has certain advantages in cost or duration. Finally, optimized transfer strategy with engineering constraints is searched out and examined to be an effective alternative solution for a given direct transfer mission. This paper investigated main methods and gave out an optimized solution in interplanetary transfer via the vicinity of libration points. Although most of Earth-Mars mission planners prefer to build up a direct transfer strategy for the mission due to its advantage in relatively short time of flight, the strategies given in the paper could still be regard as effective alternative solutions since the advantages mentioned above and longer departure window than direct transfer.

Keywords: circular restricted three-body problem, halo/Lyapunov orbit, invariant manifolds, libration points

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Authors: Kang-Mo Jung

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The use of regularization for statistical methods has become popular. The least absolute shrinkage and selection operator (LASSO) framework has become the standard tool for sparse regression. However, it is well known that the LASSO is sensitive to outliers or leverage points. We consider a new robust estimation which is composed of the weighted loss function of the pairwise difference of residuals and the adaptive penalty function regulating the tuning parameter for each variable. Rank regression is resistant to regression outliers, but not to leverage points. By adopting a weighted loss function, the proposed method is robust to leverage points of the predictor variable. Furthermore, the adaptive penalty function gives us good statistical properties in variable selection such as oracle property and consistency. We develop an efficient algorithm to compute the proposed estimator using basic functions in program R. We used an optimal tuning parameter based on the Bayesian information criterion (BIC). Numerical simulation shows that the proposed estimator is effective for analyzing real data set and contaminated data.

Keywords: adaptive penalty function, robust penalized regression, variable selection, weighted rank regression

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Authors: John Knight, Fuchun Li, Yan Xu

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Based on a new method of the nonparametric estimator of the drift function, we propose a consistent test for the parametric specification of the drift function in the short rate diffusion process using observations from a panel of yields. The test statistic is shown to follow an asymptotic normal distribution under the null hypothesis that the parametric drift function is correctly specified, and converges to infinity under the alternative. Taking the daily 7-day European rates as a proxy of the short rate, we use our test to examine whether the drift of the short rate diffusion process is linear or nonlinear, which is an unresolved important issue in the short rate modeling literature. The testing results indicate that none of the drift functions in this literature adequately captures the dynamics of the drift, but nonlinear specification performs better than the linear specification.

Keywords: diffusion process, nonparametric estimation, derivative security price, drift function and volatility function

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Authors: C. Pislaru, A. Shebani

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This paper uses the radial basis function neural network (RBFNN) for system identification of nonlinear systems. Five nonlinear systems are used to examine the activity of RBFNN in system modeling of nonlinear systems; the five nonlinear systems are dual tank system, single tank system, DC motor system, and two academic models. The feed forward method is considered in this work for modelling the non-linear dynamic models, where the K-Means clustering algorithm used in this paper to select the centers of radial basis function network, because it is reliable, offers fast convergence and can handle large data sets. The least mean square method is used to adjust the weights to the output layer, and Euclidean distance method used to measure the width of the Gaussian function.

Keywords: system identification, nonlinear systems, neural networks, radial basis function, K-means clustering algorithm

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Authors: Zhihui Liu, Dongmei Hao, Qian Qiu, Yang An, Lin Yang, Song Zhang, Yimin Yang, Xuwen Li, Dingchang Zheng

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Premature birth, defined as birth before 37 completed weeks of gestation is a leading cause of neonatal morbidity and mortality and has long-term adverse consequences for health. It has recently been reported that the worldwide preterm birth rate is around 10%. The existing measurement techniques for diagnosing preterm delivery include tocodynamometer, ultrasound and fetal fibronectin. However, they are subjective, or suffer from high measurement variability and inaccurate diagnosis and prediction of preterm labor. Electrohysterography (EHG) method based on recording of uterine electrical activity by electrodes attached to maternal abdomen, is a promising method to assess uterine activity and diagnose preterm labor. The purpose of this study is to analyze the difference of EHG signal features between term labor and preterm labor. Free access database was used with 300 signals acquired in two groups of pregnant women who delivered at term (262 cases) and preterm (38 cases). Among them, EHG signals from 38 term labor and 38 preterm labor were preprocessed with band-pass Butterworth filters of 0.08–4Hz. Then, EHG signal features were extracted, which comprised classical time domain description including root mean square and zero-crossing number, spectral parameters including peak frequency, mean frequency and median frequency, wavelet packet coefficients, autoregression (AR) model coefficients, and nonlinear measures including maximal Lyapunov exponent, sample entropy and correlation dimension. Their statistical significance for recognition of two groups of recordings was provided. The results showed that mean frequency of preterm labor was significantly smaller than term labor (p < 0.05). 5 coefficients of AR model showed significant difference between term labor and preterm labor. The maximal Lyapunov exponent of early preterm (time of recording < the 26th week of gestation) was significantly smaller than early term. The sample entropy of late preterm (time of recording > the 26th week of gestation) was significantly smaller than late term. There was no significant difference for other features between the term labor and preterm labor groups. Any future work regarding classification should therefore focus on using multiple techniques, with the mean frequency, AR coefficients, maximal Lyapunov exponent and the sample entropy being among the prime candidates. Even if these methods are not yet useful for clinical practice, they do bring the most promising indicators for the preterm labor.

Keywords: electrohysterogram, feature, preterm labor, term labor

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Authors: F. Bringby, A. Nordin, L. Björnådal, E. Svenungsson, C. Boström, H Alexanderson

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Patients with systemic sclerosis (SSc) have reduced hand function and self-reported limitations in daily activities. Few studies have explored limitations in shoulder-arm mobility and muscle function, or if there are differences in physical function between diffuse cutaneous (dcSSc) and limited cutaneous (lcSSc) SSc. The purpose of this study was to describe objectively assessed shoulder-arm mobility, lower extremity muscle function and muscle endurance in SSc and evaluate possible differences between lcSSc and dcSSc. 121 patients with SSc were included in this cross sectional study. Shoulder-arm mobility were examined using the Shoulder Function Assessment Scale (SFA) including 5 tasks ,lower extremity muscle function was measured by Timed stands test (TST) and muscle endurance in shoulder- and hip flexors were assessed by the Functional Index 2 (FI-2). Patients with dcSSc had median SFA hand to back score 5 (4-6) and median “hand to seat” score of 5 (4-6) compared to patients with lcSSc with corresponding median values of 6 (4-6) and 6 (5-6) respectively (p<0.01-p<0.05). 50% of both patientsgroups had lower muscle function assessed by the TST compared to age- and gender matched reference values but there were no differences in TST between the two patient groups. There was no difference in FI-2 scores between dcSSc and lcSSc. The whole group had 40 (28-83) % and 38 (32-72) % of maximal FI-2 shoulder flexion score on the right and left sides, and 40 (23-63) % and 37 (23-62) % of maximal FI-2 hip flexion score on the right and left sides. Reference values for the FI-2 indicate that healthy individuals perform in mean 100 % of maximal score. Patients with dcSSc were more limited than patients with lcSSc. Patients with SSc have reduced muscle function compared to reference values. These results highlights the importance of assessing shoulder-arm mobility and muscle function as well as a need for further research to identify exercise interventions to target these limitations.

Keywords: diffuse, limited, mobility, muscle function, physical therapy, systemic sclerosis

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Authors: Kenichiro Hida, Shin-Ichi Kuribayashi

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NFV-based network implements a variety of network functions with software on general-purpose servers, and this allows the network operator to select any capabilities and locations of network functions without any physical constraints. In this paper, we evaluate the influence of the maximum tolerable network delay on the virtual routing function deployment guidelines which the authors proposed previously. Our evaluation results have revealed the following: (1) the more the maximum tolerable network delay condition becomes severe, the more the number of areas where the route selection function is installed increases and the total network cost increases, (2) the higher the routing function cost relative to the circuit bandwidth cost, the increase ratio of total network cost becomes larger according to the maximum tolerable network delay condition.

Keywords: NFV (Network Functions Virtualization), resource allocation, virtual routing function, minimum total network cost

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Authors: Jalal Eddine Benmansour, Khouane Boulanoir, Nacera Bekhadda, Elhassen Benfriha

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This paper introduces a novel composite control approach that addresses the challenge of stabilizing the three-axis attitude of a flexible satellite in the presence of vibrations caused by flexible appendages. The key contribution of this research lies in the development of a disturbance observer, which effectively observes and estimates the unwanted torques induced by the vibrations. By utilizing the estimated disturbance, the proposed approach enables efficient compensation for the detrimental effects of vibrations on the satellite system. To govern the attitude angles of the spacecraft, a proportional derivative controller (PD) is specifically designed and proposed. The PD controller ensures precise control over all attitude angles, facilitating stable and accurate spacecraft maneuvering. In order to demonstrate the global stability of the system, the Lyapunov method, a well-established technique in control theory, is employed. Through rigorous analysis, the Lyapunov method verifies the convergence of system dynamics, providing strong evidence of system stability. To evaluate the performance and efficacy of the proposed control algorithm, extensive simulations are conducted. The simulation results validate the effectiveness of the combined approach, showcasing significant improvements in the stabilization and control of the satellite's attitude, even in the presence of disruptive vibrations from flexible appendages. This novel composite control approach presented in this paper contributes to the advancement of satellite attitude control techniques, offering a promising solution for achieving enhanced stability and precision in challenging operational environments.

Keywords: attitude control, flexible satellite, vibration control, disturbance observer

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

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Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: artificial immune system, breast cancer diagnosis, Euclidean function, Gaussian function

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Authors: Shun Horikoshi, Tohru Kawabe

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This study presents performance analysis results of SMC (Sliding mode control) with changing the chattering functions applied to slip suppression problem of electric vehicles (EVs). In SMC, chattering phenomenon always occurs through high frequency switching of the control inputs. It is undesirable phenomenon and degrade the control performance, since it causes the oscillations of the control inputs. Several studies have been conducted on this problem by introducing some general saturation function. However, study about whether saturation function was really best and the performance analysis when using the other functions, weren’t being done so much. Therefore, in this paper, several candidate functions for SMC are selected and control performance of candidate functions is analyzed. In the analysis, evaluation function based on the trade-off between slip suppression performance and chattering reduction performance is proposed. The analyses are conducted in several numerical simulations of slip suppression problem of EVs. Then, we can see that there is no difference of employed candidate functions in chattering reduction performance. On the other hand, in slip suppression performance, the saturation function is excellent overall. So, we conclude the saturation function is most suitable for slip suppression sliding mode control.

Keywords: sliding mode control, chattering function, electric vehicle, slip suppression, performance analysis

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Authors: Diriba Dereje

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Background: Cardiac and renal disease are the most prevalent chronic non-communicable diseases (CNCD) affecting the community in a significant manner. The best and recommended method in halting CNCD is by working on prevention as early as possible. This is only possible if early surrogate markers are identified. As part of the stated solution, this study will identify an association between microalbuminuria (an early surrogate marker of renal and cardiac disease) and lung function test among adult in the community. Objective: The main aim of this study was to assess an association between microalbuminuria (an early surrogate marker of renal and cardiac disease) and lung function test among adult in the community. Methodology: Community based cross sectional study was conducted among 384 adult in Jimma town. A systematic sampling technique was used in selecting participants to the study. In searching for the possible association, binary and multivariate logistic regression and t-test was conducted. Finally, the association between microalbuminuria and lung function test was well stated in the form of figures and written description. Result and Conclusion: A significant association was found between microalbuminuria and different lung function test parameters.

Keywords: microalbuminuria, lung function, association, test

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Authors: J. Juan Peña, J. Morales, J. García-Ravelo, J. García-Martínes

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Haruo Okabayashi

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Human biological signals (pulse wave and brain wave, etc.) have a rhythm which shows fluctuations. This study investigates the relationship between fluctuations of biological signals which are shown by a finger plethysmogram (i.e., finger pulse wave) in conversation and anthropophobic tendency, and identifies whether the fluctuation could be an index of mental health. 32 college students participated in the experiment. The finger plethysmogram of each subject was measured in the following conversation situations: Fun memory talking/listening situation and regrettable memory talking/ listening situation for three minutes each. Lyspect 3.5 was used to collect the data of the finger plethysmogram. Since Lyspect calculates the Lyapunov spectrum, it is possible to obtain the largest Lyapunov exponent (LLE). LLE is an indicator of the fluctuation and shows the degree to which a measure is going away from close proximity to the track in a dynamical system. Before the finger plethysmogram experiment, each participant took the psychological test questionnaire “Anthropophobic Scale.” The scale measures the social phobia trend close to the consciousness of social phobia. It is revealed that there is a remarkable relationship between the fluctuation of the finger plethysmography and anthropophobic tendency scale in talking about a regrettable story in conversation: The participants (N=15) who have a low anthropophobic tendency show significantly more fluctuation of finger pulse waves than the participants (N=17) who have a high anthropophobic tendency (F (1, 31) =5.66, p<0.05). That is, the participants who have a low anthropophobic tendency make conversation flexibly using large fluctuation of biological signal; on the other hand, the participants who have a high anthropophobic tendency constrain a conversation because of small fluctuation. Therefore, fluctuation is not an error but an important drive to make better relationships with others and go towards the development of interaction. In considering mental health, the fluctuation of biological signals would be an important indicator.

Keywords: anthropophobic tendency, finger plethymogram, fluctuation of biological signal, LLE

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Authors: Ruhugül Özge Ocak, Banu Öztürk Kurtaslan

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Botanical gardens are very significant organizations which protect the environment against the increasing environmental problems, provide environmental education for people, offer recreation possibilities, etc. This article describes botanical gardens and their functions. The most important function of a botanical garden is to provide environmental education for people and improve environmental awareness. Considering this function, some botanical gardens were examined and opinions were suggested about the subject.

Keywords: botanical garden, environment, environmental education, recreation

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Authors: Ali Dorostkar

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In this paper, a basic schematic of fractional dimensional optimization problem is presented. As will be shown, a method is performed based on a relation between roots and tangent lines of function in fractional dimensions for an arbitrary initial point. It is shown that for each polynomial function with order N at least N tangent lines must be existed in fractional dimensions of 0 < α < N+1 which pass exactly through the all roots of the proposed function. Geometrical analysis of tangent lines in fractional dimensions is also presented to clarify more intuitively the proposed method. Results show that with an appropriate selection of fractional dimensions, we can directly find the roots. Method is presented for giving a different direction of optimization problems by the use of fractional dimensions.

Keywords: tangent line, fractional dimension, root, optimization problem

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Authors: Y. Long, L. Liu, K. V. Branin

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One challenge faced by procurement decision-maker during the acquisition process is how to compare similar products from different suppliers and allocate orders among different products or services. This work focuses on allocating orders among multiple suppliers considering rebate. The objective function is to minimize the total acquisition cost including purchasing cost and rebate benefit. Rebate benefit is complex and difficult to estimate at the ordering step. Rebate rules vary for different suppliers and usually change over time. In this work, we developed a system to collect the rebate policies, standardized the rebate policies and developed two-stage optimization models for ordering allocation. Rebate policy with multi-tiers is considered in modeling. The discontinuous cost function of rebate benefit is formulated for different scenarios. A piecewise linear function is used to approximate the discontinuous cost function of rebate benefit. And a Mixed Integer Programing (MIP) model is built for order allocation problem with multi-tier rebate. A case study is presented and it shows that our optimization model can reduce the total acquisition cost by considering rebate rules.

Keywords: discontinuous cost function, mixed integer programming, optimization, procurement, rebate

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Authors: Shahed Vahedi, Mohd Salmi Md Noorani

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This paper investigates cluster synchronization phenomena between community networks. We focus on the situation where a variety of dynamics occur in the clusters. In particular, we show that different synchronization states simultaneously occur between the networks. The controller is designed having an adaptive control gain, and theoretical results are derived via Lyapunov stability. Simulations on well-known dynamical systems are provided to elucidate our results.

Keywords: cluster synchronization, adaptive control, community network, simulation

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Authors: Ying Li, Yan Li

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A new algorithm for single hidden layer feedforward neural networks (SLFN), Orthogonal Basis Extreme Learning (OBEL) algorithm, is proposed and the algorithm derivation is given in the paper. The algorithm can decide both the NNs parameters and the neuron number of hidden layer(s) during training while providing extreme fast learning speed. It will provide a practical way to develop NNs. The simulation results of function approximation showed that the algorithm is effective and feasible with good accuracy and adaptability.

Keywords: neural network, orthogonal basis extreme learning, function approximation

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