AUT Journal of Mathematics and Computing
https://ajmc.aut.ac.ir/
AUT Journal of Mathematics and Computingendaily1Mon, 01 Jul 2024 00:00:00 +0330Mon, 01 Jul 2024 00:00:00 +0330An iterative scheme for a class of generalized Sylvester matrix equations
https://ajmc.aut.ac.ir/article_5358.html
In this study based on the accelerated over relaxation (AOR) method we make an iterative scheme for solving generalized Lyapunov matrix equation$$ {A}{X}+{X}{B}+\sum_{j=1}^{m}{N}_j{X}{M}_j={C},$$over complex or real matrices. Then we analyze the convergence of the new iterative method in detail. There have been discussions for the calculation of optimal parameters. Finally a numerical example is given to demonstrate the capability of the new method.Strong domination number of a modified graph
https://ajmc.aut.ac.ir/article_5207.html
Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $\deg(x)\leq \deg(y)$. The strong domination number $\gamma_{\rm st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on $\gamma_{\rm st}(G)$ when $G$ is modified by operations on vertices and edges of $G$.On biprojectivity and Connes biprojectivity of a dual Banach algebra with respect to a $w^*$ -closed ideal
https://ajmc.aut.ac.ir/article_5164.html
In this paper, we introduce a notion of Connes biprojectivity for a dual Banach algebra $A$ with respect to its $w^{*}$-closed ideal $I$, say $I$-Connes biprojectivity. Some Lipschitz algebras $Lip_{\alpha}(X)$ and some matrix algebras are studied under this new notion. Also, with some mild assumptions, the relation between $I$-Connes biprojectivity and left $\phi$-contractibility is given, where $\phi$ is a $w^{*}$-continuous multiplicative linear functional on $A$. As an application, we characterize Connes biprojectivity of some Lipschitz algebras.Text steganography by changing the black color
https://ajmc.aut.ac.ir/article_5177.html
Recently, a serious problem in communications is security. Hiding data is one of the most important security techniques. Steganography is the art and science of hiding information in a cover media. Texts are the most usual method of communication and so they are very suitable for cover objects. In this paper, we give a new technique for text steganography. There exist different models, such as RGB, HSL, HSV to determine a color. The main goal of the proposed algorithm is the fact that some different but very similar colors in RGB have the same code in HSL. We use this fact to hide data. For this purpose, first we find a color B&prime; in RGB, which is very similar to black in such a way that they have the same code in HSL. Then, by changing the color of each character of the text to black or B&prime;, we conceal the information. We will show that the capacity of this method is better than some other methods of text steganography, and then we show that the invisibility of this algorithm is very high, which is the most prominent feature of the proposed technique.Almost Ricci soliton in $Q^{m^{\ast}}$
https://ajmc.aut.ac.ir/article_5190.html
In this paper, we will focus our attention on the structure of $h$-almost Ricci solitons on complex hyperbolic quadric. We will prove non-existence a contact real hypersurface in the complex hyperbolic quadric $Q^{m^*}, m\geq 3$, admitting the gradient almost Ricci soliton. Moreover, the gradient almost Ricci soliton function $f$ is trivial.Variational problem, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation
https://ajmc.aut.ac.ir/article_5197.html
The goal of this article is to compute conservation law, Lagrangian and $\mu$-conservation law of the generalized Rosenau-type equation using the homotopy operator, the $\mu$-symmetry method and the variational problem method. The generalized Rosenau-type equation includes the generalized Rosenau equation, the generalized Rosenau-RLW equation and the generalized Rosenau-KdV equation, which admits the third-order Lagrangian. The article also compares the conservation law and the $\mu$-conservation law of these three equation.&nbsp;Existence and convergence of fixed points for noncyclic $\varphi$-contractions
https://ajmc.aut.ac.ir/article_5171.html
In the paper, we introduce a new class of noncyclic $\varphi$-contractions as a generalization of the class of noncyclic contractions which was first introduced in the paper [R. Esp&acute;ınola, M. Gabeleh, On the structure of minimal sets of relatively nonexpansive mappings, Numerical Functional Analysis and Optimization 34 (8), 845-860, 2013] and study the existence, uniqueness and convergence of a fixed point for such class of noncyclic mapping in the framework of uniformly convex Banach spaces. We obtain existence results of the best proximity points for cyclic $\varphi$-contractions as a consequence of our main theorems.Interpolatory four-parametric adaptive method with memory for solving nonlinear equations
https://ajmc.aut.ac.ir/article_5248.html
The adaptive technique enables us to achieve the highest efficiency index theoretically and practically. The idea of introducing an adaptive self-accelerator (via all the old information for Steffensen-type methods) is new and efficient to obtain the highest efficiency index. In this work, we have used four self-accelerating parameters and have increased the order of convergence from 8 to 16, i. e. any new function evaluations improve the convergence order up to 100%. The numerical results are compared without and with memory methods. It confirms that the proposed methods have more efficiency index.Generalized Lorentz Ricci solitons on $3$-dimensional Lie groups associated to Bott connection
https://ajmc.aut.ac.ir/article_5195.html
In this paper, we investigate which one of the non-isometric left-invariant Lorentz metrics $g$ on $3$-dimensional Lie groups satisfies the generalized Ricci soliton equation $a{\rm Ric}^B [g] + \dfrac{b}{2}{\cal L}_{ X}^B g +cX^\flat\otimes X^\flat = \lambda g$ associated to the Bott connection $\nabla^B$, here ${X}$ is a vector field and $\lambda , a, b, c$ are real constants such that $c\neq 0$. A complete classification of this structure on $3$-dimensional Lorentzian Lie groups will be presented.Composition operators from Zygmund spaces into Besov Zygmund-type spaces
https://ajmc.aut.ac.ir/article_5211.html
&lrm;In this paper first&lrm;, &lrm;the boundedness and compactness of a composition operator from Zygmund space to Besov Zygmund-type space are studied&lrm;. &lrm;Then we study this concepts for this operator by using the hyperbolic-type analytic Besov Zygmund-type class&lrm;. &lrm;Finally&lrm;, &lrm;we show the relation between the hyperbolic-type analytic Besov Zygmund-type class and the meromorphic (or spherical) Besov Zygmund-type class&lrm;.Lipschitzness effect of a loss function on generalization performance of deep neural networks trained by Adam and AdamW optimizers
https://ajmc.aut.ac.ir/article_5213.html
The generalization performance of deep neural networks with regard to the optimization algorithm is one of the major concerns in machine learning. This performance can be affected by various factors. In this paper, we theoretically prove that the Lipschitz constant of a loss function is an important factor to diminish the generalization error of the output model obtained by Adam or AdamW. The results can be used as a guideline for choosing the loss function when the optimization algorithm is Adam or AdamW. In addition, to evaluate the theoretical bound in a practical setting, we choose the human age estimation problem in computer vision. For assessing the generalization better, the training and test datasets are drawn from different distributions. Our experimental evaluation shows that the loss function with a lower Lipschitz constant and maximum value improves the generalization of the model trained by Adam or AdamW.Driver cellphone usage detection using wavelet scattering and convolutional neural networks
https://ajmc.aut.ac.ir/article_5229.html
This paper provides an automated system based on machine learning and computer vision to detect cellphone usage during driving. We used Wavelet Scattering Networks, which is a simple and efficient type of architecture. The presented model is straightforward and compact and requires little hyper-parameter tuning. The speed of this model is similar to the Convolutional Neural Networks. We monitored the driver from two viewpoints: a frontal view of the driver&rsquo;s face and a side view of the driver&rsquo;s whole body. We created a new dataset for the first viewpoint, and used a publicly available dataset for the second viewpoint. Our model achieved the test accuracy of 91% for our new dataset and 99% for the publicly available one.A survey on usage of smartphone accelerometer sensor in intelligent transportation systems
https://ajmc.aut.ac.ir/article_5238.html
The numerous capabilities of smartphones have made them suitable alternative to expensive tools and methods in intelligent transportation systems. This study surveys the literature on the role of the accelerometer of smartphones in intelligent transportation applications. At first, the opportunities and challenges of using the accelerometer are stated. Then, the architecture of using this sensor including preprocessing, feature extraction, mode detection, reorientation and applications are explained. Finally, different applications that have used the accelerometer of mobile phones in the intelligent transportation systems have been investigated.Some results concerning asymptotic distribution of functional linear regression with points of impact
https://ajmc.aut.ac.ir/article_5255.html
Lately, issues related to functional linear regression models with points of impact have garnered significant interest. While the literature has addressed the estimation of parameters for this model with scalar response, less attention has been paid to the asymptotic distribution of the impact points coefficients estimators. In recent literature, the asymptotic distribution has been pointed out in a particular case, but the demonstration of its validity has not been adequately addressed. By explicating the necessary requirements, we derive an important part of the asymptotic distribution of the impact points coefficients estimators in a general setting. This is a fundamental result for finding the asymptotic distribution of the impact points coefficients estimators. Moreover, we perform a simulation study to exhibit the efficiency of the obtained results.$K$-contact generalized square Finsler manifolds
https://ajmc.aut.ac.ir/article_5257.html
We study almost contact generalized square Finsler manifolds and introduce the notion of $K$-contact Finsler structures. Then, we characterize generalized square $K$-contact almost contact manifolds. As an application, we show that every $3$-dimensional Lie group admits a left-invariant generalized square Finsler structure.Exploring the use of efficient deep learning algorithms for lower grade gliomas cancer MRI image segmentation: A case study
https://ajmc.aut.ac.ir/article_5261.html
This paper presents a study on the use of efficient deep learning algorithms for lower grade gliomas (LGG) cancer image segmentation. The study compares the performance of various pretrained atrous-convolutional architectures and pre-trained U-Nets, and proposes a transformer-based approach for fast and efficient LGG segmentation. The study evaluated the performance of various models and found that DeepLabV3+ with MobileNetV3 as a backbone achieved the best per-formance among the pretrained models. However, the proposed transformer-based approach surpassed the aforementioned methods and achieved competitive results with higher scores. The study also employed transfer learning techniques to fine-tune the pretrained models on the LGG dataset, which significantly im-proved segmentation performance with a relatively low amount of training samples. The study highlights the importance of selecting the appropriate pre-trained model for the specific segmentation task. The proposed transformer-based approach offers several advantages over traditional convolutional neural networks, including efficient use of memory and better generalization. It can also process images of arbitrary sizes, making it more flexible and scalable for use in clinical settings. Segmenting medical images presents a difficult task because of the complexity of medical images and variations in imaging conditions. The use of efficient deep learning algorithms can help address these challenges by reducing computational cost, training time, and improving segmentation performance. The findings of this study can be useful in the development of accurate and efficient diagnostic tools for LGG cancer detection and treatment planning. The proposed transformer-based approach has the potential to improve medical image segmentation for other types of cancers and diseases. Overall, this study demonstrates the potential impact of deep learning and transfer learning application in medical image segmentation, with significant implications for improving cancer diagnosis and treatment.A novel mobile robot path planning method based on neuro-fuzzy controller
https://ajmc.aut.ac.ir/article_5262.html
In recent years, the navigation of mobile robots has been of great interest. One of the important challenges in the navigation of mobile robots is the obstacle avoidance problem so that the robots do not collide with each other and obstacles, during their movement. Hence, for good navigation, a reliable obstacle avoidance methodology is needed. On the other hand, some of the other most important challenges in robot control are in the field of motion planning. The main goal of motion planning is to compile (interpret) high-level languages into a series of primary low-level movements. In this paper, a novel online sensor-based motion planning algorithm that employs the Adaptive Neuro-Fuzzy Inference System (ANFIS) controller is proposed. Also, this algorithm is able to distance the robots from the obstacles (i.e. it provides a solution to the obstacle avoidance problem). In the proposed motion planning algorithm, three distances (i.e. the distance of the robot from the obstacles in three directions: right, left, and front) have been used to prioritize the goal search behavior and obstacle avoidance behavior and to determine the appropriate angle of rotation. Then, for determining the linear velocity, the nearest distance from obstacles and distance from the goal have been used. The proposed motion planning algorithm has been implemented in the gazebo simulator (by using Turtlebot) and its performance has been evaluated. Finally, to improve the performance of the proposed motion planning algorithm, We have used type-1, interval type-2, and interval type-3 fuzzy sets, then, we have evaluated and compared the efficiency of the proposed algorithm for each of these fuzzy sets under specific criteria.A distributionally robust approach for the risk-parity portfolio selection problem
https://ajmc.aut.ac.ir/article_5269.html
Risk-parity is one of the most recent and interesting strategies in the portfolio selection area. Considering the mean-standard-deviation risk measure, this paper studies the risk-parity problem under the uncertainty of the covariance matrix. Assuming that the uncertainty is represented by a finite set of scenarios, the problem is formulated as a scenario-based stochastic programming model. Then, since the occurrence probabilities of scenarios are not known with certainty, two ambiguity sets of distributions are considered, and corresponding to each one, a distributionally robust optimization model is presented. Computational experiments on real-world instances taken from the literature confirm the importance of the proposed models in terms of stability, volatility and Sharpe-ratio.Finding the extreme efficient solutions of multi-objective pseudo-convex programming problems
https://ajmc.aut.ac.ir/article_5280.html
In this paper, we present two methods to find the strictly efficient and weakly efficient points of multi-objective programming (MOP) problems in which their objective functions are pseudo-convex and their feasible sets are polyhedrons. the obtained efficient solutions in these methods are the extreme points. Since the pseudo-convex functions are quasi-convex as well, therefore the presented methods can be used to find efficient solutions of the (MOP) problem with the quasi-convex objective functions and the polyhedron feasible set. Two experimental examples are presented.Two-stage stochastic capacitated lot-sizing problem by lot-size adaptation approach
https://ajmc.aut.ac.ir/article_5281.html
In this paper, a two-stage stochastic capacitated lot-sizing problem with random demand, and service level constraints under static and static-dynamic uncertainty strategies is introduced. A static strategy determines the setup period and lot sizing at the beginning of planning period, whereas a static-dynamic strategy allows the lot size to be adjusted during the planning period. A new model formulation of the demand differential adjustment policy in a multi-stage production system is proposed. Lot-sizing adjustments depend on the difference in demand between actual and expected demand. To quantify the economics of our uncertainty strategy for multi-level lot size the problems, the number of test instances with different parameter settings is evaluated. Computational experiments show that the additional costs of semi-finished products, and the lack of storage capacity in the downstream processes reduce the potential for cost savings via multi-volume reform. Also a robust model is developed and as the robust model under study is NP-hard, it solved by a hybrid heuristic using the proposed stochastic model, a robust model is developed, which is solved by a hybrid heuristic algorithm based on Lagrangian relaxation and Bender's decomposition algorithms. To evaluate the convergence rate and solution quality, the method is applied to some random test instances generated in the literature. The computational results indicate that the proposed method is capable of efficiently solving the model.$C^*$-algebra-valued $S_b$-metric spaces and applications to integral equations
https://ajmc.aut.ac.ir/article_5282.html
We first introduce the concept of $C^*$-algebra-valued $S_{b}$-metric space, then we prove Banach contraction principle in this space. Finally, existence and uniqueness results for one type of integral equation is discussed.An efficient computational approach for numerical solution of non-smooth dynamical systems
https://ajmc.aut.ac.ir/article_5286.html
In this paper, an efficient computational approach based on the fantastic Simpson integral formula is developed for the numerical solution of non-smooth dynamical equations. In the proposed approach, at first, the integral reformulation of the target problem is intended. Then, the Simpson formula is employed to discretize the obtained integral equation. It is mentioned that, the implementation of the method is simple, so, the method can be simply and quickly used to solve a wide variety of non-smooth dynamical systems arising in the various engineering models. Numerical experiments of two benchmark examples are presented at the end and the efficiency of the method is reported.Structure of Clifford-Weyl algebras and representations of ortho-symplectic Lie superalgebras
https://ajmc.aut.ac.ir/article_5310.html
In this article, the structure of the Clifford-Weyl superalgebras and their associated Lie superalgebras will be investigated. These superalgebras have a natural supersymmetric inner product which is invariant under their Lie superalgebra structures. The Clifford-Weyl superalgebras can be realized as tensor product of the algebra of alternating and symmetric tensors respectively, on the even and odd parts of their underlying superspace. For Physical applications in elementary particles, we add star structures to these algebras and investigate the basic relations. Ortho-symplectic Lie algebras are naturally present in these algebras and their representations on these algebras can be described easily.On conformal transformation of $\Xi$-curvature
https://ajmc.aut.ac.ir/article_5316.html
In this paper, we study the conformal transformation of recent defined non-Riemannian curvature in Finsler Geometry, namely $\Xi$-curvature. Indeed, we obtain the necessary and sufficient condition under which the conformal transformation preserves the $\Xi$-curvature.A remark on the metric dimension in Riemannian manifolds of constant curvature
https://ajmc.aut.ac.ir/article_5326.html
We compute the metric dimension of Riemannian manifolds of constant curvature. We define the edge weighted metricdimension of the geodesic graphs in Riemannian manifolds and we show that each complete geodesic graph $G = (V,E)$ embedded in a Riemannin manifold of constant curvature resolves a totally geodesic submanifold of dimension $|V| &minus; 1$.Perfectness of the essential graph for modules over commutative rings
https://ajmc.aut.ac.ir/article_5327.html
&lrm;Let $R$ be a commutative ring and $M$ be an $R$-module&lrm;. &lrm;The essential graph of $M$&lrm;, &lrm;denoted by $EG(M)$ is a simple graph with vertex set $Z(M) \setminus {\rm{Ann}}_R(M)$ and two&lrm; &lrm;distinct vertices $x,y \in Z(M) \setminus {\rm{Ann}}_R(M)$ are adjacent if and only if&lrm; &lrm;${\rm{Ann}}_M(xy)$ is an essential submodule of $M$&lrm;. &lrm;In this paper&lrm;, &lrm;we investigate&lrm; &lrm;the dominating set&lrm;, &lrm;the clique and the chromatic numbers and the metric dimension&lrm; &lrm;of the essential graph for Noetherian modules&lrm;. &lrm;Let&lrm; &lrm;$M$ be a Noetherian $R$-module such that $\mid {\rm MinAss}_R(M)\mid=n\geq 2$&lrm; &lrm;and let $EG(M)$ be a connected graph&lrm;. &lrm;We prove that&lrm; &lrm;$EG(M)$ is weakly prefect, &lrm;that is&lrm;, $\omega(EG(M))=\chi(EG(M))$&lrm;. Furthermore&lrm;, it is shown that ${\rm dim}(EG(M))=\mid Z(M)\mid-(\mid {\rm{Ann}}(M)\mid+2^n)$, whenever $r({\rm{Ann}}(M) )\neq{\rm{Ann}}(M)$ and ${\rm dim}(EG(M))=\mid Z(M)\mid-(\mid {\rm{Ann}}(M)\mid+2^n-2)$&lrm;, whenever $r({\rm{Ann}}(M) )= {\rm{Ann}}(M)$&lrm;.Analysis of the vacuum solution of the five-dimensional Einstein field equations with negative cosmological constant via variational symmetries
https://ajmc.aut.ac.ir/article_5329.html
The Kaluza-Klein theory can be reckoned as a classical unified field theory of two of the significant forces of nature gravitation and electromagnetism. This formulation geometrically demonstrates the effects of a gravitational and an electromagnetic field by investigating a five-dimensional space with a metric constructed via the spacetime metric and the four-potential of the electromagnetic field. For the purpose of exploring the influences of dimensionality on the distinct physical variables, inquiring into stationary Kaluza-Klein rotating fluids is of particular significance. In this research, an extensive investigation of the variational symmetries for a specific vacuum solution of the (4+1)-dimensional Einstein field equations with negative cosmological constant is presented. For this purpose, first of all, the variational symmetries of our analyzed model are completely determined and the construction of the Lie algebra of the resulted symmetries is accurately analyzed. It is represented that the Lie algebra of local symmetries interrelated to the system of geodesic equations is non-solvable and not semi-simple and the algebraic organization of the derived quotient Lie algebra is accurately evaluated. Mainly, the adjoint representation group is effectively utilized intended for establishing an optimal system of group invariant solutions; which unequivocally yields a conjugate relation in the set of all one-dimensional symmetry subalgebras. Accordingly, the associated set of invariant solutions can be regarded as the slightest list from that the alternative invariant solutions of one-dimensional subalgebras are thoroughly determined unambiguously by virtue of transformations. Literally, all the corresponding local conservation laws of the resulted variational symmetries are totally calculated. Indeed, the symmetries of the metric of our analyzed space-time lead to the constants of motion for the point particles.Dynamic monopolies in simple graphs
https://ajmc.aut.ac.ir/article_5350.html
This paper studies a repetitive polling game played on an $n$-vertex graph $G$. At first, each vertex is colored, Black or White. At each round, each vertex (simultaneously) recolors itself by the color of the majority of its closed neighborhood. The variants of the model differ in the choice of a particular tie-breaking rule. We assume the tie-breaking rule is Prefer-White and we study the relation between the notion of ``dynamic monopoly" and ``vertex cover" of $G$. In particular, we show that any vertex cover of $G$ is a dynamic monopoly or reaches a $2-$periodic coloring. Moreover, we compute $\rm{dyn}(G)$ for some special classes of graphs including paths, cycles and links of some graphs.A new relaxation technique based on fractional representation to solve bilinear models: Application to the long horizon crude oil scheduling problem
https://ajmc.aut.ac.ir/article_5357.html
This paper proposes a novel relaxation technique based on the fractional representation of bilinear terms. This technique is embedded into an iterative two-step MILP-NLP algorithm based on piecewise relaxation and domain reduction strategies. To evaluate the performance of the algorithm, it is compared to the recently addressed iterative MILP-NLP algorithm based on piecewise McCormick relaxation techniques over a variety of instances. Our method is also applied to the crude oil scheduling problem as an application. The results confirm the efficiency of the proposed algorithm from both solution quality and running time.A secure method of voting and planning based on quadratic voting
https://ajmc.aut.ac.ir/article_5367.html
Recently, an innovative voting method named quadratic voting (QV) has been proposed which allows people to vote as much as they want, according to the intensity of their preferences. Little research has been done on the safe implementation of this method. In this paper, we first present a voting method based on QV. This method combines voting and planning and gives the ability to voters to express their opinions about the candidate&rsquo;s programs in addition to voting. Then, a secure electronic voting protocol is proposed for implementing the given method. This protocol gives the voters to check the verifiability of ballots and the safety of payment so that they would be sure that their votes are counted correctly.Machine learning approach for bipolar disorder analysis and recognition based on handwriting digital images
https://ajmc.aut.ac.ir/article_5383.html
In some cases, handwriting is a manifestation of the human mind, and it can reveal various psychological characteristics and mental disorders. Among these disorders, bipolar disorder is a well-known and widely studied condition in cognitive science and psychotherapy, and it can be detected in handwriting. In this research, we applied image processing techniques to analyze the handwriting characteristics of people with bipolar disorder based on their responses to a survey. We also proposed a machine learning model that can classify whether a person has bipolar disorder or not by using their handwriting as an input.Left $\phi$-biflatness and $\phi$-biprojectivity of certain Banach algebras with applications
https://ajmc.aut.ac.ir/article_5384.html
This paper continues the investigation initially begun for left $\phi$-biflatness and left $\phi$-biprojectivity. We show that left $\phi$-biflatness and left $\phi$-biprojectivity are closely related to the notions of left $\phi$-amenability and $\phi$-inner amenability. We characterize left $\phi$-biprojectivity and left $\phi$-biflatness of certain semigroup algebras and some algebras related to a locally compact group. We discuss non left $\phi$-biflatness of some specified triangular Banach algebras.A new characterization of Chevalley groups $\mathbf{G_2(3^n)}$ by the order of the group and the number of elements with the same order
https://ajmc.aut.ac.ir/article_5385.html
In this paper, we prove that chevalley groups $G_2(q)$, where $q=3^n$ and $q^2+q+1$ is a prime numbers can be uniquely determined by the order of group and the number of elements with the same order.Power study of goodness of fit tests for the Rayleigh distribution based on the empirical distribution function with application to real data
https://ajmc.aut.ac.ir/article_5397.html
The Rayleigh distribution is widely used to model events that occur in different fields such as medicine and natural sciences. In this article, we suggest some test statistics for examining the Rayleigh goodness of fit based on the empirical distribution function. Critical points and power of the tests are obtained by Monte Carlo simulation. We show that the proposed tests have a good performance against different alternatives and therefore these tests can be confidently used in practice. Finally, the proposed tests are illustrated by real data examples.On Zermelo’s navigation problem and weighted Einstein Randers metrics
https://ajmc.aut.ac.ir/article_5403.html
This paper investigates a specific form of weighted Ricci curvature known as the quasi-Einstein metric. Two Finsler metrics, $F$ and $\tilde{F}$ are considered, which are generated by navigation representations $(h, W)$ and $(F, V)$, respectively, where $W$ represents a vector field, and $V$ represents a conformal vector field on the manifold $M$. The main focus is on identifying the necessary and sufficient condition for the Randers metric $F$ to qualify as a quasi-Einstein metric. Additionally; we establish the relationship between the curvatures of the given Finsler metrics $F$ and $\tilde{F}$.The competition of robust methods in linear and nonlinear regression with heavy-tailed stable errors
https://ajmc.aut.ac.ir/article_5404.html
Robust regression methods including Least Trimmed Squares are one of the most important methodologies to compute exact coeﬃcient estimators when data is polluted with outliers. There is interest to generalize Least Trimmed Squares for regression models with heavy-tailed stable errors. In this manuscript, we compare estimating coeﬃcients methods with the robust Least Trimmed Squares method in stable errors case. Therefore, we propose Stable Least Trimmed Squares and Nonlinear Stable Least Trimmed Squares methods for linear/nonlinear regression models with stable errors, respectively. The joint distribution of ordered errors is used with the ﬁnite variance property of ordered stable errors, whose indexes are deﬁned by cut-oﬀ points. We make many comparisons using simulated and real datasets.An existence result for a Robin problem involving $p(x)$-Kirchhoff-type equation with indefinite weight
https://ajmc.aut.ac.ir/article_5412.html
This paper discusses the existence of nontrivial weak solutions for a class of $p(x)$-Kirchhoff-type equation plus an indefinite potential under Robin boundary condition. The variable exponent theory of generalized Lebesgue-Sobolev spaces, mountain pass theorem and Ekeland variational principle are used for this purpose.The chi-square statistic as an income inequality index
https://ajmc.aut.ac.ir/article_5413.html
This article presents a novel concept known as the chi-square inequality index, developed through the utilization of the chi-square distance function. The study delves into the essential characteristics necessary for an effective inequality index. Additionally, a detailed formulation for the chi-square inequality curve is provided within key inequality models. A comparative analysis between the chi-square curve and the conventional Lorenz curve is conducted. Furthermore, a stochastic order based on the chi-square inequality curve is introduced. The research includes a simulation analysis to explore the statistical properties of the proposed sampling estimator. To conclude, the article highlights the effectiveness of this index through an application to real-world data.DRP-VEM: Drug Repositioning Using Voting Ensemble Model
https://ajmc.aut.ac.ir/article_5429.html
Conventional approaches to drug discovery are both expensive and time-intensive. To circumvent these challenges, drug repurposing or repositioning (DR) has emerged as a prevalent strategy. A noteworthy advancement in this field involves the widespread application of machine learning techniques. The effectiveness of these methods depends on the quality of features, their representations, and the underlying dataset. Notably, the issue of redundancy in feature sets can detrimentally impact the overall performance of these methods. Furthermore, the careful selection of a suitable training set plays a pivotal role in enhancing the accuracy of machine learning approaches in addressing drug repurposing challenges. Discovering the appropriate training set faces two significant challenges. Firstly, many methods utilize known drug-disease pairs for positives and unknown pairs for negatives. The stark imbalance in the number of known and unknown pairs often results in a bias towards the larger group, introducing errors in machine learning performance. Secondly, the absence of a documented drug-disease association indicates that it hasn&#039;t been experimentally approved yet, and this status may change in the future.
This paper introduces DRP-VEM, a novel approach designed for predicting drug repositioning, specifically customized to tackle the challenges previously outlined. DRP-VEM evaluates the effectiveness of binary-based and similarity-based representations of drugs and diseases in enhancing the model&#039;s performance. Additionally, it proposes a voting ensemble training strategy, adept at managing imbalanced datasets. The assessment of DRP-VEM spans a range of parameters, including its efficacy in representing both diseases and drugs, the proficiency of its classification methods, and the application of voting ensemble training approaches using heterogeneous evaluation criteria. Significantly, DRP-VEM achieves an AUC-ROC of 81.8% and AUC-PR of 76.6%. Comparative analysis with other studies highlights the superior performance of the proposed model, underscoring its effectiveness in drug repositioning prediction.Co-even Domination Number of a Modified Graph by Operations on a Vertex or an Edge
https://ajmc.aut.ac.ir/article_5457.html
Let $G=(V,E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$.
The cardinality of a smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. A dominating set $D$ is called co-even dominating set if the degree of vertex $v$ is even number for all $v\in V-D$.
The cardinality of a smallest co-even dominating set of $G$, denoted by $\gamma _{coe}(G)$, is the co-even domination number of $G$.
In this paper, we study co-even domination number of graphs which constructed by some operations on a vertex or an edge of a graph.SCAD Regression Model Selection with Information Criteria for Multivariate Response Models
https://ajmc.aut.ac.ir/article_5460.html
This paper provides an objective function for smoothly clipped absolute deviation (SCAD) regression models with multivariate responses. The log-likelihood of a multivariate normal distribution is considered instead of L2 norm to create the model&rsquo;s objective function. Additionally, the SCAD penalty has a tuning parameter, and the information criteria, suitable for the proposed model are presented to select the tuning parameter. Based on numerical studies, the consistency of the proposed information criteria is checked via simulation experiments. Moreover, the best criterion is introduced using simulated and real datasets.