Search results for: Bessel function

Authors: Zuhier Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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Authors: Bina Kumari, Subir K. Sarkar, Pradipta Bandyopadhyay

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The autocorrelation function of the density fluctuation is studied in each of the two phases in a Gibbs Ensemble Monte Carlo (GEMC) simulation of the problem of phase separation for a square well potential with various values of its range. We find that the normalized autocorrelation function is described very well as a linear combination of an exponential function with a time scale τ₂ and a stretched exponential function with a time scale τ₁ and an exponent α. Dependence of (α, τ₁, τ₂) on the parameters of the GEMC algorithm and the range of the square well potential is investigated and interpreted. We also analyse the issue of how to choose the parameters of the GEMC simulation optimally.

Keywords: autocorrelation function, density fluctuation, GEMC, simulation

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Authors: Yuan Zheng

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3D model-based vehicle matching provides a new way for vehicle recognition, localization and tracking. Its key is to construct an evaluation function, also called fitness function, to measure the degree of vehicle matching. The existing fitness functions often poorly perform when the clutter and occlusion exist in traffic scenarios. In this paper, we present a practical and efficient fitness function. Unlike the existing evaluation functions, the proposed fitness function is to study the vehicle matching problem from both local and global perspectives, which exploits the pixel gradient information as well as the silhouette information. In view of the discrepancy between 3D vehicle model and real vehicle, a weighting strategy is introduced to differently treat the fitting of the model’s wireframes. Additionally, a normalization operation for the model’s projection is performed to improve the accuracy of the matching. Experimental results on real traffic videos reveal that the proposed fitness function is efficient and robust to the cluttered background and partial occlusion.

Keywords: 3D-2D matching, fitness function, 3D vehicle model, local image gradient, silhouette information

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Authors: Mohammedi Ferhate

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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.

Keywords: function, operator, simulation, wave

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Authors: Md. Rashidul Hasan, Atikur Rahman Baizid

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The Bayesian estimation approach is a non-classical estimation technique in statistical inference and is very useful in real world situation. The aim of this paper is to study the Bayes estimators of the parameter of exponential distribution under different loss functions and then compared among them as well as with the classical estimator named maximum likelihood estimator (MLE). In our real life, we always try to minimize the loss and we also want to gather some prior information (distribution) about the problem to solve it accurately. Here the gamma prior is used as the prior distribution of exponential distribution for finding the Bayes estimator. In our study, we also used different symmetric and asymmetric loss functions such as squared error loss function, quadratic loss function, modified linear exponential (MLINEX) loss function and non-linear exponential (NLINEX) loss function. Finally, mean square error (MSE) of the estimators are obtained and then presented graphically.

Keywords: Bayes estimator, maximum likelihood estimator (MLE), modified linear exponential (MLINEX) loss function, Squared Error (SE) loss function, non-linear exponential (NLINEX) loss function

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Authors: Jihad H. Asad

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An expression for the Green’s function (GF) of anisotropic face cantered cubic (IFCC) lattice is evaluated analytically and numerically for a single impurity problem. The density of states (DOS), phase shift and scattering cross section are expressed in terms of complete elliptic integrals of the first kind.

Keywords: lattice Green's function, elliptic integral, physics, cubic lattice

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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: 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: 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: 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

Abstract:

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-Martínez

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sᵩ 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: Ghizlane Barzi, Zineb Bamousse

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In an increasingly volatile global economic context characterized by recurring crises, the financial function of companies is called upon to play a strategic role not only in resource management but also in organizational resilience. The emergence of financial technologies (fintech) offers innovative tools capable of transforming this function by enhancing the efficiency of financial processes and increasing companies' ability to adapt and overcome economic shocks. However, despite the rapid rise of fintechs and their growing adoption by companies, there remain uncertainties regarding the real impact of these innovations on the financial resilience of organizations. Indeed, how do fintech-driven innovations transform the financial function, and to what extent does this transformation contribute to strengthening the financial resilience of companies in the face of contemporary crises? This research aims to explore these questions by examining the interrelationships between the financial function, fintech innovations, and corporate resilience, in order to identify optimization levers that could be adopted for better financial risk management.

Keywords: finance, financial function, fintech, resilience, innovation

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Authors: Ruhugül Özge Ocak, Banu Öztürk Kurtaslan

Abstract:

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

Abstract:

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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