Real Vector Research Articles

HYBRID BINARY WHALE OPTIMIZATION ALGORITHM BASED ON TAPER SHAPED TRANSFER FUNCTION FOR SOFTWARE DEFECT PREDICTION

Reliability is one of the key factors used to gauge software quality. Software defect prediction (SDP) is one of the most important factors which affects measuring software's reliability. Additionally, the high dimensionality of the features has a direct effect on the accuracy of SDP models. The objective of this paper is to propose a hybrid binary whale optimization algorithm (BWOA) based on taper-shape transfer functions for solving feature selection problems and dimension reduction with a KNN classifier as a new software defect prediction method. In this paper, the values of a real vector that represents the individual encoding have been converted to binary vector by using the four types of Taper-shaped transfer functions to enhance the performance of BWOA to reduce the dimension of the search space. The performance of the suggested method (T-BWOA-KNN) was evaluated using eleven standard software defect prediction datasets from the PROMISE and NASA repositories depending on the K-Nearest Neighbor (KNN) classifier. Seven evaluation metrics have been used to assess the effectiveness of the suggested method. The experimental results have shown that the performance of T-BWOA-KNN produced promising results compared to other methods including ten methods from the literature, four types of T-BWOA with the KNN classifier. In addition, the obtained results are compared and analyzed with other methods from the literature in terms of the average number of selected features (SF) and accuracy rate (ACC) using the Kendall W test. In this paper, a new hybrid software defect prediction method called T-BWOA-KNN has been proposed which is concerned with the feature selection problem. The experimental results have proved that T-BWOA-KNN produced promising performance compared with other methods for most datasets.

A DIFFERENTIABLE STRUCTURE ON A FINITE DIMENSIONAL REAL VECTOR SPACE AS A MANIFOLD

There are three conditions for a topological space to be said a topological manifold of dimension : Hausdorff space, second-countable, and the existence of homeomorphism of a neighborhood of each point to an open subset of or -dimensional locally Euclidean. The differentiable structure is given if the intersection of two charts is an empty chart or its transition map is differentiable. In this article, we study a differentiable manifold on finite dimensional real vector spaces. The aim is to prove that any finite-dimensional vector space is a differentiable manifold. First of all, it is proved that a finite dimensional vector space is a topological manifold by constructing a norm as its topology. Given a metric which is induced by a norm. Two norms on a finite dimensional vector space are always equivalent and they are determine the same topology. Secondly, it is proved that the transition map in the finite dimensional vector space is differentiable. As conclusion, we have that any finite dimensional vector space with independent norm topology choice is a differentiable manifold. As a matter of discussion, it can be studied that the vector space of all linear operators of a finite dimensional vector space has a differentiable manifold structure as well.

A solution potential-based adaptation reference vector evolutionary algorithm for many-objective optimization

Decomposition-based multiobjective evolutionary algorithms are widely utilized for solving multiobjective optimization problems (MOPs). These algorithms have a higher degree of diversity due to a uniform distribution of the reference vectors in the objective space. However, these algorithms may struggle to select a suitable candidate set for solving many-objective optimization problems (MaOPs) with irregular Pareto fronts (PFs). To solve this problem, a solution potential-based adaptation reference vector evolutionary algorithm (SPARVEA) is proposed in this paper. In the algorithm, a concept called solution potential is presented to assess whether the direction of convergence of the solution to the ideal solution has potential. The solution potential is obtained with an evaluation function to calculate the potentials of the corresponding solutions. A solution potential-based adaptation strategy is then designed for adapting the reference vector to better guide the direction of convergence of the solution when solving MaOPs with irregular PFs. A modified angle penalty distance (mAPD) is adjusted to improve the convergence rate of the solution set in many-objective optimization problems. The proposed algorithm SPARVEA is compared with state-of-the-art many-objective evolutionary algorithms on four test sets with irregular PFs and four practical problems. Experimental results demonstrate the superior performance of SPARVEA on many-objective optimization problems. This contribution helps to advance the development of efficient algorithms for solving many-objective optimization problems.

Disease2Vec: Encoding Alzheimer’s progression via disease embedding tree

For decades, a variety of predictive approaches have been proposed and evaluated in terms of their prediction capability for Alzheimer’s Disease (AD) and its precursor – mild cognitive impairment (MCI). Most of them focused on prediction or identification of statistical differences among different clinical groups or phases, especially in the context of binary or multi-class classification. The continuous nature of AD development and transition states between successive AD related stages have been typically overlooked. Though a few progression models of AD have been studied recently, they were mainly designed to determine and compare the order of specific biomarkers. How to effectively predict the individual patient’s status within a wide spectrum of continuous AD progression has been largely understudied. In this work, we developed a novel learning-based embedding framework to encode the intrinsic relations among AD related clinical stages by a set of meaningful embedding vectors in the latent space (Disease2Vec). We named this process as disease embedding. By Disease2Vec, our framework generates a disease embedding tree (DETree) which effectively represents different clinical stages as a tree trajectory reflecting AD progression and thus can be used to predict clinical status by projecting individuals onto this continuous trajectory. Through this model, DETree can not only perform efficient and accurate prediction for patients at any stages of AD development (across five fine-grained clinical groups instead of typical two groups), but also provide richer status information by examining the projecting locations within a wide and continuous AD progression process. (Code will be available: https://github.com/qidianzl/Disease2Vec.)

On the Problem of Tension Forces Distribution in Cable System of Cable-Driven Parallel Robot

The paper proposes a method for controlling tension forces in statically indeterminable cable-driven systems based on the non-negative least squares method with control of singular or near-singular solutions and a complete search of all possible cable configurations. For cable-driven parallel robots the problem of controlling the cable tension forces is critical, because in the absence of control the cable tension forces are distributed unevenly, which leads to reduced robustness of the system, increased energy consumption and increased deterioration. And in special cases of cable system configuration the tension forces become so great that they lead to cable breaks. At the same time, correction of cable tension force distribution should not lead to significant deviations from the specified position of the mobile platform or, formulating the problem in terms of forces, to violation of kinetostatic equations. Thus, the problem of controlling the tension forces in the cable parallel robot system is solved as a problem of optimizing the tension forces of the cables according to the criteria of minimizing the norm of their vector in the configuration space and minimizing the norm of incoherence of the vector of forces and moments in the operational space of the robot. The developed algorithm is based on the solution of underdetermined systems of linear algebraic equations with finding the minimum least squares norms and subsequent zeroing of negative components of the solution vector. The paper considers examples of the solution of the set problem for the lower cable group of a construction 3D printer based on a cable-driven robot and for a 12-cable system

DeepWalk with Reinforcement Learning (DWRL) for node embedding

DeepWalk is used to convert nodes in an original graph into equivalent vectors in a latent space for performing various predictive tasks. To ensure second-order structural similarity between nodes in the original graph and their vectors in the latent space, dot products are applied to each pair of nodes explored on the random walk (RW) in the latent space. However. dot products for graphs with millions of nodes and billions of edges are computationally expensive. To minimize the computation time required for calculating the second-order structural similarity, DeepWalk with reinforcement learning (DWRL) is proposed herein. In DWRL, a level pointer for each node in the original graph is prepared. By identifying common nodes between each pair of nodes in the original graph, the number of computations in the dot product in the latent space is reduced, thereby ensuring second-order structural similarity. Additionally, repeated selection of the same node during RWs produces redundant samples for training. Therefore, the subsampling technique is used to choose the next node based on its degree, which improves the generalization of node representations in the latent space and increases accuracy. The proposed techniques are applied to popular datasets to perform multilabel classification and link prediction tasks, and their efficiency in reducing the computation time is verified. The proposed DWRL minimizes the computation time 47% for large graphs to build latent vectors and improves the average micro and macro F1 scores up to 12%. The link prediction performance also increases up to 20%.

Complex Representation Learning with Graph Convolutional Networks for Knowledge Graph Alignment

The task of discovering equivalent entities in knowledge graphs (KGs), so-called KG entity alignment, has drawn much attention to overcome the incompleteness problem of KGs. The majority of existing techniques learns the pointwise representations of entities in the Euclidean space with translation assumption and graph neural network approaches. However, real vectors inherently neglect the complex relation structures and lack the expressiveness of embeddings; hence, they may guide the embeddings to be falsely generated which results in alignment performance degradation. To overcome these problems, we propose a novel KG alignment framework, ComplexGCN, which learns the embeddings of both entities and relations in complex spaces while capturing both semantic and neighborhood information simultaneously. The proposed model ensures richer expressiveness and more accurate embeddings by successfully capturing various relation structures in complex spaces with high-level computation. The model further incorporates relation label and direction information with a low degree of freedom. To compare our proposal against the state-of-the-art baseline techniques, we conducted extensive experiments on real-world datasets. The empirical results show the efficiency and effectiveness of the proposed method.

Some geometric properties of the Padovan vectors in Euclidean 3-space

Padovan numbers were defined by Stewart (1996) in honor of the modern architect Richard Padovan (1935) and were first discovered in 1924 by Gerard Cordonnier. Padovan numbers are a special status of Tribonacci numbers with initial conditions and general terms. The ratio between Padovan numbers is one of the important algebraic numbers because it produces plastic numbers. Up to now, various studies have been conducted on Padovan numbers and Padovan polynomial sequences. In this study, Padovan vectors are defined for the first time by using the Padovan Binet-like formula and reduction relation. Then, geometric properties of Padovan vectors such as inner product, norm, and vector products are analyzed. In the last part of the study, Padovan vectors were calculated with Binet formulas in the Geogebra program. In addition, the first ten Padovan numbers and Padovan vectors were calculated using the Binet formulas and shown as points and vectors in three-dimensional space. According to the Padovan vectors found, the Padovan curve was drawn in space for the first time by using the curve fitting feature of the Geogebra program. Thus, with our study, a geometric approach to Padovan number sequences was brought for the first time.

Two-Phase Model Predictive Direct Duty-Cycle Control for PMSM With Off-Line Lookup Table

Finite control set model predictive control has poor steady-state performance due to limited voltage vectors. To improve the steady-state performance, multiple vectors are used to synthesize more accurate voltage vectors, but the selection of optimal vectors is always complex. In this paper, a two-phase model predictive direct duty-cycle control based on off-line lookup table (OLT) is constructed. The proposed prediction model converts three-phase duty cycles to two-phase duty cycles, which reduces the number of duty cycles calculations. In addition, to optimize the reference voltage vectors space, a new flux linkage deviation mechanism is proposed where the virtual reference vectors can be determined with low complexity by using OLT. Then, due to further improve the steady-state accuracy and ensure low complexity, a new flux linkage constraint is proposed, which restricts the flux linkage while reducing the torque ripple. More importantly, no weight factor is needed to balance the torque and stator flux. Finally, the process of the multi-stage and multi-duty-cycle calculation is converted into the process of a one-stage and small range single-variable enumeration selection, which significantly reduces calculation cost while improving the steady-state performance. The feasibility and effectiveness ofthe proposed method isverified bytheoryand experiments.

Transfluthrin diffusers do not protect two-person US military tents from mosquitoes in open field and canopy warm-temperate habitats

Spatial repellents are volatile or volatilized chemicals that may repel arthropod vectors in free space, preventing bites and reducing the potential for pathogen transmission. In a 21-week field study, we investigated the efficacy of passive transfluthrin-impregnated diffusers placed in two-person United States (US) military tents located in canopy and open field habitats in north Florida to prevent mosquitoes from entering. Mosquito collections with US Centers for Disease Control and Prevention traps baited with light and carbon dioxide were conducted weekly for weeks 0–4, every two weeks for weeks 5–10, and monthly for weeks 11–21. Our results demonstrated that these transfluthrin-impregnated devices did not function as spatial repellents as expected and did not create a mosquito-free zone of protection. Instead, we observed consistently higher collections of mosquitoes from tents with transfluthrin-impregnated diffusers, and higher rates of mosquito mortality in collections from tents with transfluthrin diffusers, compared to untreated control tents. Based on these findings we do not recommend the use of passive transfluthrin-impregnated diffusers for mosquito protection in two-person US military tents in warm-temperate environments similar to north Florida.

An implicit Z-bus based sequential power flow algorithm for VSC AC/DC systems

AC/DC power flow algorithms have been proposed and developed as essential analysis tools for the Voltage Source Converter (VSC) based AC/DC hybrid grid. However, prevailing AC/DC power flow algorithms, e.g., the Newton-Raphson based algorithm, suffer from limitations in terms of convergence, multiple solutions, and high computational complexity. To address these issues, this paper presents a novel sequential AC/DC power flow algorithm based on the implicit Z-bus (IZB) method. We firstly provide a general AC/DC power flow model in real vector space, which takes into account the interface data, internal connection and various control modes of VSC stations. Then, simple and compact IZB iterative mappings in real vector space are derived for the AC solver and DC solver. A sequential algorithmic architecture and data exchange mechanisms are designed considering losses calculation, capacity limits and control strategy switching. The impacts of tolerance settings, initial value selections and load levels on the convergence and accuracy of the algorithm are theoretically analysed. Notably, rigorous convergence analyses substantiate the superior attributes of the proposed algorithm over existing models, guaranteeing convergence to high-voltage solutions (feasible and stable solutions). Numerical tests are performed to compare the proposed algorithm with existing works in terms of accuracy, efficiency, scalability and reliability.

Parametric Lie group structures on the probabilistic simplex and generalized Compositional Data

In this paper we build a set of parametric quotient Lie group structures on the probabilistic simplex that can be extended to real vector space structures. In particular, we rediscover the main mathematical objects generally used when treating compositional data as elements associated to the quotient Lie group with respect to the equivalence relation induced by the scale invariance principle. This perspective facilitates the adaptation of the statistical methods used for classical compositional data to data that follows a more general equivalence relation.

Turrittin's normal forms for linear systems of meromorphic ODEs over the real field

We establish a version of Turrittin's result on normal forms of linear systems of meromorphic ODEs when the base field K is real and closed. Both the proposed normal forms and the transformations used have coefficients in K. Our motivation comes from applications to the study of trajectories of real analytic vector fields (already treated in the literature in dimension three). For the sake of clarity and completeness, we first review Turrittin's theorem in the case of an algebraically closed base field. For more information see https://ejde.math.txstate.edu/Volumes/2023/79/abstr.html

Predicting Tipping Points in a Family of PWL Systems: Detecting Multistability via Linear Operators Properties

The study of dynamical systems is based on the solution of differential equations that may exhibit various behaviors, such as fixed points, limit cycles, periodic, quasi-periodic attractors, chaotic behavior, and coexistence of attractors, to name a few. In this paper, we present a simple and novel method for predicting the occurrence of tipping points in a family of Piece-Wise Linear systems (PWL) that exhibit a transition from monostability to multistability with the variation of a single parameter, without the need to compute time series, i.e., without solving the differential equations of the system. The linearized system of the model is analyzed, the stable and unstable manifolds are taken to be real vectors in space, and the changes suffered by these vectors as a result of the modification of the parameter are examined using such simple metrics as the magnitude of a vector or the angle between two vectors in space. The results obtained with the linear analysis of the system agree well with those obtained with the numerical resolution of the dynamical system itself. The work presented here is an extension of previous results on this topic and contributes to the understanding of the mechanisms by which a system changes its stability by fragmenting its basin of attraction. This, in turn, enriches the field by providing an alternative to numerical resolution to identify quantitative changes in the dynamics of complex systems without having to solve the differential equation system.

APTM: Structurally Informative Network Representation Learning

Network representation learning algorithms provide a method to map complex network data into low-dimensional real vectors, aiming to capture and preserve structural information within the network. In recent years, these algorithms have found widespread applications in tasks such as link prediction and node classification in graph data mining. In this work, we propose a novel algorithm based on an adaptive transfer probability matrix. We use a deep neural network, comprising an autoencoder, to encode and reduce the dimensionality of the generated matrix, thereby encoding the intricate structural information of the network into low-dimensional real vectors. We evaluate the algorithm's performance through node classification, and in comparison with mainstream network representation learning algorithms, our proposed algorithm demonstrates favorable results. It outperforms baseline models in terms of micro-F1 scores on three datasets: PPI, Citeseer, and Wiki.

Exceptional points in periodic array of silicon rods

We find numerically the complex eigenvalues in grating composed of infinitely long silicon rods of rectangular cross section and show existence of exceptional points (EPs) in parametric space of structural scales and wave vector along the rods. The EPs have sufficiently small imaginary parts due to their proximity to bound states in the continuum. This enables to trace the resonant frequencies in the transmission around the EP and, accordingly, to identify the EP by bifurcation of the transmission. We present generic coupled mode theory to elucidate this effect. We also show that structural fluctuations of grating preserve EP but obscures their observation because of inhomogeneous broadening of transmission peaks.

A partition-based problem transformation algorithm for classifying imbalanced multi-label data

Multi-label learning has garnered much research interest due to its wide range of real-world applications. Many multi-label learning methods have been proposed; however, few have addressed the class imbalance problem existing in multi-label data. Even though some studies have taken this issue into account, most of them have ignored the label correlations or only considered random correlations between them. In this study, we propose a novel partition-based imbalanced multi-label learning algorithm, named Multi-label Learning based on Hierarchical Clustering (MLHC), to tackle this problem. MLHC first carries out hierarchical clustering on the original label space to divide it into several disconnected subspaces, each of which contains several labels that are strongly correlated with each other. Then, for each label subspace, we use the problem transformation strategy to convert it into a multi-class problem by binary coding. Any multi-class imbalance learning algorithm can be applied to the transformed multi-class data. Finally, the classification results will be decoded to retrieve the corresponding label subspace, and all label subspace results are combined to show the predicted label vector in the original label space. We conducted experiments not only on thirteen benchmark multi-label datasets but also carried out them on XJTU-SY which is a multi-label engineering application dataset, and the results indicated that our proposed MLHC learning algorithm outperforms several state-of-the-art class imbalance multi-label learning algorithms, demonstrating the effectiveness and necessity of discovering label correlations and transforming the original imbalanced multi-label learning problem into multiple strongly correlated multi-class imbalanced learning problems.

Vector bundles on real abelian varieties

This paper is about real holomorphic vector bundles on real abelian varieties. The main result of the paper gives several conditions that are necessary and sufficient for the existence of a holomorphic connection on a real holomorphic vector bundle over a real abelian variety. Also proved is an analogue, for real abelian varieties, of a result of Simpson, which gives a criterion for a holomorphic vector bundle to arise by successive extensions of stable vector bundles with vanishing Chern classes.

Non-equilibrium dynamics of dipole-charged fields in the Proca theory

We discuss the dynamics of field configurations encoded in the certain class of electric (magnetic) dipole-charged states in the Proca theory of the real massive vector field. We construct such states so as to ensure that the long-distance structure of the mean electromagnetic field in them is initially set by the formula describing the electromagnetic field of the electric (magnetic) dipole. We analyze then how such a mean electromagnetic field evolves in time. We find that far away from the center of the initial field configuration, the long-range component of the mean electromagnetic field harmonically oscillates, which leads to the phenomenon of the periodic oscillations of the electric (magnetic) dipole moment. We also find that near the center of the initial field configuration, the mean electromagnetic field escapes from its initial arrangement and a spherical shock wave propagating with the speed of light appears in the studied system. A curious configuration of the axisymmetric mean electric field is found to accompany the mean magnetic field in magnetic dipole-charged states.

Predicting drug-drug interactions based on multi-view and multichannel attention deep learning.

Predicting drug-drug interactions (DDIs) has become a major concern in the drug research field because it helps explore the pharmacological function of drugs and enables the development of new therapeutic drugs. Existing prediction methods simply integrate multiple drug attributes or perform tasks on a biomedical knowledge graph (KG). Though effective, few methods can fully utilize multi-source drug data information. In this paper, a multi-view and multichannel attention deep learning (MMADL) model is proposed, which not only extracts rich drug features containing both drug attributes and drug-related entity information from multi-source databases, but also considers the consistency and complementarity of different drug feature representation learning approaches to improve the effectiveness and accuracy of DDI prediction. A single-layer perceptron encoder is applied to encode multi-source drug information to obtain multi-view drug representation vectors in the same linear space. Then, the multichannel attention mechanism is introduced to obtain the attention weight by adaptively learning the importance of drug features according to their contributions to DDI prediction. Further, the representation vectors of multi-view drug pairs with attention weights are used as inputs of the deep neural network to predict potential DDI. The accuracy and precision-recall curves of MMADL are 93.05 and 95.94, respectively. The results indicate that the proposed method outperforms other state-of-the-art methods.