Real Vector Research Articles

Exploring the Features and Trends of Industrial Product E-Commerce in China Using Text-Mining Approaches

Industrial product e-commerce refers to the specific application of the e-commerce concept in industrial product transactions. It enables industrial enterprises to conduct transactions via Internet platforms and reduce circulation and operating costs. Industrial literature, such as policies, reports, and standards related to industrial product e-commerce, contains much crucial information. Through a systematical analysis of this information, we can explore and comprehend the development characteristics and trends of industrial product e-commerce. To this end, 18 policy documents, 10 industrial reports, and five standards are analyzed by employing text-mining methods. Firstly, natural language processing (NLP) technology is utilized to pre-process the text data related to industrial product commerce. Then, word frequency statistics and TF-IDF keyword extraction are performed, and the word frequency statistics are visually represented. Subsequently, the feature set is obtained by combining these processes with the manual screening method. The original text corpus is used as the training set by employing the skip-gram model in Word2Vec, and the feature words are transformed into word vectors in the multi-dimensional space. The K-means algorithm is used to cluster the feature words into groups. The latent Dirichlet allocation (LDA) method is then utilized to further group and discover the features. The text-mining results provide evidence for the development characteristics and trends of industrial product e-commerce in China.

Sparse Bayesian Learning Based Multi Trajectory Tracking Algorithm For Direction of Arrival Trajectory Estimation

One of the applications of sequential sparse signal reconstruction is multi-target Direction of Arrival (DoA) trajectory estimation. In fact, each member of the support set is equivalent to the DoA of a moving target at each time instant. There is a mapping between the indices of the sparse vector and DoA values in continuous angle space. The key idea of this paper is to use the dynamic information of the continuous angular space to more accurately track sparse vectors and estimate the DoA trajectories of moving sources with time-varying acceleration based on the Sparse Bayesian Learning (SBL) framework. For this purpose, the members of the estimated support set are mapped to the continuous angular space at each instant. Then, the obtained DoAs are assigned to the available DoA trajectories using the Predictive-Description-Length (PDL) algorithm. In the following, the DoA of each source is predicted for the next time using the Kalman filter. Finally, the predicted DoAs are mapped to a sparse vector. The obtained sparse vector is used as the prior information for SBL-based sparse reconstruction. Simulation results show that the proposed algorithm, which is called SBL-MTT (Multi Trajectory Tracking), leads to an accurate reconstruction of successive sparse vectors in application of DoA trajectory estimation of moving sources.

Neural Vector Fields for Implicit Surface Representation and Inference

AbstractNeural implicit fields have recently shown increasing success in representing, learning and analysis of 3D shapes. Signed distance fields and occupancy fields are still the preferred choice of implicit representations with well-studied properties, despite their restriction to closed surfaces. With neural networks, unsigned distance fields as well as several other variations and training principles have been proposed with the goal to represent all classes of shapes. In this paper, we develop a novel and yet a fundamental representation considering unit vectors in 3D space and call it Vector Field (VF). At each point in $$\mathbb {R}^3$$ R 3 , VF is directed to the closest point on the surface. We theoretically demonstrate that VF can be easily transformed to surface density by computing the flux density. Unlike other standard representations, VF directly encodes an important physical property of the surface, its normal. We further show the advantages of VF representation, in learning open, closed, or multi-layered surfaces. We show that, thanks to the continuity property of the neural optimization with VF, a separate distance field becomes unnecessary for extracting surfaces from the implicit field via Marching Cubes. We compare our method on several datasets including ShapeNet where the proposed new neural implicit field shows superior accuracy in representing any type of shape, outperforming other standard methods. Codes are available at https://github.com/edomel/ImplicitVF.

Characterizations of complex P-matrices

A P-matrix is a square matrix all of whose principal minors are positive. The characterization of real P-matrices as matrices that do not reverse the sign of any nonzero real vector is generalized to complex P-matrices by associating them with the reflection of complex vectors. This prompts the extension of other P-matrix properties and related real matrix classes to the complex field. In particular, semipositivity of real P-matrices is generalized to complex P-matrices. Principal pivot transforms and Cayley transforms of complex P-matrices are also considered.

Distributional hypothesis as isomorphism between word-word co-occurrence and analogical parallelograms.

Most of the modern natural language processing (NLP) techniques are based on the vector space models of language, in which each word is represented by a vector in a high dimensional space. One of the earliest successes was demonstrated by the four-term analogical reasoning task: what is to C as B is to A? The trained word vectors form "parallelograms" representing the quadruple of words in analogy. This discovery in NLP offers us insight into our understanding of human semantic representation of words via analogical reasoning. Despite successful applications of the large-scale language models, it has not been fully understood why such parallelograms emerge by learning through natural language data. As the vector space model is not optimized to form parallelograms, the key structure related to geometric shapes of word vectors is expected to be in the data, rather than the models. In the present article, we test our hypothesis that such parallelogram arrangement of word vectors readily exists in the co-occurrence statistics of language. Our approach focuses more on the data itself, and it is different from the existing theoretical approach trying to find the mechanism of parallelogram formation in the algorithms and/or vector arithmetic operations on word vectors. First, our analysis suggested that analogical reasoning is possible by decomposition of the bigram co-occurrence matrix. Second, we demonstrated the formation of a parallelepiped, a more structured geometric object than a parallelogram, by creating a small artificial corpus and its word vectors. With these results, we propose a refined form of distributional hypothesis pointing out an isomorphism between a sort of symmetry or exchangeability and word co-occurrence statistics.

Characterization of continuous additive set-valued maps “modulo K” on finite dimensional linear spaces

Abstract Let Y be a real vector metric space and K ⊂ Y be a closed convex cone such that K ∩ (− K) = {0}. We prove that a convex compact-valued map F : ℝ → 2 Y ∖ {∅} is K-continuous and K-additive if and only if there are non-empty convex compact sets A, B ⊂ Y such that 0 ∈ A − B ⊂ K and F is equal “modulo K” to the continuous set-valued map G ( t ) = t A , t ≥ 0 , t B , t < 0. $$\begin{array}{} \displaystyle G(t)=\begin{cases} tA,&t\geq0,\\ tB,& t \lt 0. \end{cases} \end{array}$$ Next, we use this result to characterize convex compact-valued maps F : ℝ N → 2 Y ∖ {∅}.

Dual-perspective multi-instance embedding learning with adaptive density distribution mining

Multi-instance learning (MIL) is a potent framework for solving weakly supervised problems, with bags containing multiple instances. Various embedding methods convert each bag into a vector in the new feature space based on a representative bag or instance, aiming to extract useful information from the bag. However, since the distribution of instances is related to labels, these methods rely solely on the overall perspective embedding without considering the different distribution characteristics, which will conflate the varied distributions of instances and thus lead to poor classification performance. In this paper, we propose the dual-perspective multi-instance embedding learning with adaptive density distribution mining (DPMIL) algorithm with three new techniques. First, the mutual instance selection technique consists of adaptive density distribution mining and discriminative evaluation. The distribution characteristics of negative instances and heterogeneous instance dissimilarity are effectively exploited to obtain instances with strong representativeness. Second, the embedding technique mines two crucial information of the bag simultaneously. Bags are converted into sequence invariant vectors according to the dual-perspective such that the distinguishability is maintained. Finally, the ensemble technique trains a batch of classifiers. The final model is obtained by weighted voting with the contribution of the dual-perspective embedding information. The experimental results demonstrate that the DPMIL algorithm has higher average accuracy than other compared algorithms, especially on web datasets.

QUALIMETRIC MODEL OF A HIGH-TECH INFORMATION AND MEASURING SYSTEM FOR THE PREPARATION AND CONDUCT OF TESTS

The issue of the report concerns the selection of information and testing equipment or a system that will be used for planning and conducting tests with minimal error and high efficiency. The complexity of consideration as a whole, when choosing the components of the information and measurement system and determining the qualitative measurement model determines the need to divide it into several stages and consider them separately. The stages of building a qualitative model of a high-tech information and measurement system for preparing and conducting tests are divided into: modeling stage; design stage; stage of implementation; interpretation stage. At the stage of determining the limitations, it should be taken into account in which division the tests are carried out, namely: by purpose; by the level of testing; by stages of product development; by testing finished products; according to the conditions and venue; by the duration of the tests; by type of action; by the result of the action; according to the characteristics of the object. The relevance of the work is the consideration of the stages of building a qualitative model of the information and measurement system in the difficult conditions of the military and political situation in Ukraine. The purpose of the work is to develop the technological aspects of qualitative modeling, as well as the stages of qualitative model examination. Additional results of the work can be – to obtain initial data (parameters); – to break down important indicators (parameters) according to their importance using an expert method; – to assess state and foreign requirements for the system for further work; – to assess and choose a direction based on the price indicator (factor) and duration of work or other indicators; – provide recommendations for making a decision regarding the construction of a qualitative model of the properties of the information and measurement system;–allow to improve (apply) the process of conducting tests of high-tech weapons and military equipment; – allow to use qualitative model databases to reduce preparation time to conducting tests of high-tech weapons and military equipment;–will allow to expand the directions for finding new features and providing recommendations in the further process of tests. The article builds a qualitative model (hereafter KM) of the formation (creation) of KM stages of the information and measurement system (hereafter IMS) at the preparatory stage of OVT tests. Stages of KM examination have been developed based on the current purpose of the tests, the required quantity and quality of recorded and measured indicators, the complexity of measurements and their analysis. Formulated KM efficiency indicators are as follows: minimal error; cost of equipment; equipment resource; others. The stages of selection of IBS components have been developed and the KM of assessment at the preparatory stage of tests has been determined. A model of quantitative quality measurement has been developed, taking into account possible errors and the provided, structural, technological aspects and stages of qualitative modeling. The most expedient tool for a systematic approach to decision-making during the construction of the IBS CM has been determined. The results of a similar review of literary sources of domestic and foreign scientists are presented. However, the insufficient development of the scientific basis for creating KM efficiency indicators is noted. The normative and real vectors of the creation of the CM are determined, which are laid down as important indicators of the effectiveness of the CM, by changing which it is possible to change the direction of the selection of the creation of the CM of the IAS.

A cardiac audio classification method based on image expression of multidimensional features.

Heart sound auscultation plays a crucial role in the early diagnosis of cardiovascular diseases. In recent years, great achievements have been made in the automatic classification of heart sounds, but most methods are based on segmentation features and traditional classifiers and do not fully exploit existing deep networks. This paper proposes a cardiac audio classification method based on image expression of multidimensional features (CACIEMDF). First, a 102-dimensional feature vector is designed by combining the characteristics of heart sound data in the time domain, frequency domain and statistical domain. Based on the feature vector, a two-dimensional feature projection space is constructed by PCA dimensionality reduction and the convex hull algorithm, and 102 pairs of coordinate representations of the feature vector in the two-dimensional space are calculated. Each one-dimensional component of the feature vector corresponds to a pair of 2D coordinate representations. Finally, the one-dimensional feature component value and its divergence into categories are used to fill the three channels of a color image, and a Gaussian model is used to dye the image to enrich its content. The color image is sent to a deep network such as ResNet50 for classification. In this paper, three public heart sound datasets are fused, and experiments are conducted using the above methods. The results show that for the two-classification/five-classification task of heart sounds, the method in this paper can achieve a classification accuracy of 95.68%/94.53% when combined with the current deep network.

QSIM: A Quantum-inspired hierarchical semantic interaction model for text classification

Semantic interaction modeling is a fundamental technology in natural language understanding that guides models to extract deep semantic information from text. Currently, the attention mechanism is one of the most effective techniques in semantic interaction modeling, which learns word-level attention representation by measuring the relevance between different words. However, the attention mechanism is limited to word-level semantic interaction, it cannot meet the needs of fine-grained interactive information for some text classification tasks. In recent years, quantum-inspired language modeling methods have successfully constructed quantized representations of language systems in Hilbert spaces, which use density matrices to achieve fine-grained semantic interaction modeling.This paper presents a Quantum-inspired hierarchical Semantic Interaction Model (QSIM), which follows the sememe-word-sentence language construction principle and utilizes quantum entanglement theory to capture hierarchical semantic interaction information in Hilbert space. Our work builds on the idea of the attention mechanism and extends it. Specifically, we explore the original semantic space from a quantum theory perspective and derive the core semantic space using the Schmidt decomposition technique, where: (1) Sememe is represented as the unit vector in the two-dimensional minimum semantic space; (2) Word is represented as reduced density matrices in the core semantic space, where Schmidt coefficients quantify sememe-level semantic interaction. Compared to density matrices, reduced density matrices capture fine-grained semantic interaction information with lower computational cost; (3) Sentence is represented as quantum superposition states of words, and the degree of word-level semantic interaction is measured using entanglement entropy.To evaluate the model’s performance, we conducted experiments on 15 text classification datasets. The experimental results demonstrate that our model is superior to classical neural network models and traditional quantum-inspired language models. Furthermore, the experiment also confirms two distinct advantages of QISM: (1) flexibility, as it can be integrated into various mainstream neural network text classification architectures; and (2) practicability, as it alleviates the problem of parameter growth inherent in density matrix calculation in quantum language model.

A Lightweight Model Enhancing Facial Expression Recognition with Spatial Bias and Cosine-Harmony Loss

This paper proposes a facial expression recognition network called the Lightweight Facial Network with Spatial Bias (LFNSB). The LFNSB model effectively balances model complexity and recognition accuracy. It has two key components: a lightweight feature extraction network (LFN) and a Spatial Bias (SB) module for aggregating global information. The LFN introduces combined channel operations and depth-wise convolution techniques, effectively reducing the number of parameters while enhancing feature representation capability. The Spatial Bias module enables the model to focus on local facial features while capturing the dependencies between different facial regions. Additionally, a new loss function called Cosine-Harmony Loss is designed. This function optimizes the relative positions of feature vectors in high-dimensional space, resulting in better feature separation and clustering. Experimental results on the AffectNet and RAF-DB datasets demonstrate that the LFNSB model achieves competitive recognition accuracy, with 63.12% accuracy on AffectNet-8, 66.57% accuracy on AffectNet-7, and 91.07% accuracy on RAF-DB, while significantly reducing the model complexity.

$\mathfrak{sl}_{2}$ Triples Whose Nilpositive Elements Are in a Space Which Is Spanned by the Real Root Vectors in Rank 2 Symmetric Hyperbolic Kac–Moody Lie Algebras

In analogy with the theory of nilpotent orbits in finite-dimensional semisimple Lie algebras, it is known that the principal \mathfrak{sl}_{2} subalgebras can be constructed in hyperbolic Kac–Moody Lie algebras. We obtained a series of \mathfrak{sl}_{2} subalgebras in rank 2 symmetric hyperbolic Kac–Moody Lie algebras by extending the aforementioned construction. We present this result and also discuss \mathfrak{sl}_{2} modules obtained by the action of the \mathfrak{sl}_{2} subalgebras on the original Lie algebras.

Optimal Strictly Stealthy Attack Design on Cyber-Physical Systems: A Data-Driven Approach.

In this article, an issue of data-driven optimal strictly stealthy attack design for the stochastic linear invariant systems is investigated, with the aim of maximizing the system performance degradation under an energy bounded constraint and bypassing the parity-space-based attack detector. Importantly, the proposed attack policy refrains from the assumption that the system knowledge is known to attackers. A novel strictly stealthy attack sequence (SSAS), coordinating the sensor and actuator signals simultaneously, is proposed with a sufficient and necessary condition for the existence of such an attack presented. Specifically, the SSAS is parameterized as a vector in the null space of a specific matrix which is constructed by a parity matrix and the system Markov parameters. For the purpose of data-driven attack realization, modified subspace identification methods are utilized to achieve an unbiased estimation of the required parameters via the closed-loop data. On this basis, the attack design is formulated as a constrained optimization problem, an explicit solution to which is given to characterize the optimal strictly stealthy attack. Finally, the vulnerability of the cyber-physical systems is analysed from the perspective of the parameter selection for the parity space-based detector. A case study on a three-tank model verifies the efficiency of the proposed approach.

Flow field characteristics and vibration responses of saddle-shaped membrane structures

Elastically mounted flexible membrane roofs exposed to flows are prone to vortex-induced vibrations and even aero-instability due to the strong fluid–structure interaction (FSI). This study is to investigate the FSI mechanism in the saddle-shaped membrane structure over a range of Reynolds numbers and wind directions in laminar flows, by bridging structural vibration responses and flow dynamics. The aeroelastic characteristics of membrane structures, including statistics of displacement responses, oscillation frequency, and oscillation damping ratios, were identified from the perspective of time and frequency domains. Simultaneously, the particle image velocimetry system was employed to visualize the flow features, including velocity vector, turbulence intensity, and vortex evolution in both space and time. The flow modes were further decomposed by proper orthogonal decomposition (POD) to capture the salient aspects of the flow. Three patterns of POD modes are identified, and the first mode plays the dominant role in POD modes. It showed that as the wind Reynolds number increases, the space between the shear layer and membrane surface would be narrowed, and resultantly the vortices turn out smaller in scale and closer in space. This trend leads to an increase in the frequency of vortex shedding and a stronger FSI effect. When the frequency of vortex shedding approaches the fundamental frequency of structures, the vibration of the membrane would be shifted from turbulent buffeting to vortex-induced resonance, featured with lock-in frequency, significant amplified displacement, and negative aerodynamic damping ratio.

BIG DATA, BUSINESS PROCESSES, AND MATHEMATICAL ALGORITHMS FOR MULTI-OBJECTIVE MANAGERIAL DECISION OPTIMIZATION

The use of Big Data and the engineering of business processes are becoming increasingly important for managing the business of companies and large international corporate groups. For more successful outcomes, even for complex interventions such as those of the PNRR (National Recovery and Resilience Plan), the use of mathematical models to assist management decisions represents a significant lever to optimize time, costs, and planned overall performance. This analytical approach strengthens traditional qualitative techniques like SWOT analysis and finds useful application in the optimal definition of any form of PPP (Public-Private Partnership), such as the recent “Partnership for Innovation” (PPI) included in the new procurement code. The scientific work developed from the systematic analysis of processes proposes a particular multi-objective mathematical model that uses a system of vectors in an m-dimensional reference space.

Some Applications of Cauchy-Schwarz Inequality on Lightlike Warped Product Submanifolds

The well-known Cauchy-Schwarz inequality is a fundamental tool of analysis in Hilbert spaces. It is an upper bound on the inner product between two vectors in an inner product space in terms of the product of the vector norms. It is the most important and widely used inequalities in mathematics. We explore that inequality in case of lightlike warped product hypersurface of lorentzian space form to reach to the existence of minimal screen conformal lightlike hypersurface.

Surfaces with Central Configuration and Dulac’s Problem for a Three Dimensional Isolated Hopf Singularity

AbstractLet $$\xi $$ ξ be a real analytic vector field with an elementary isolated singularity at $$0\in \mathbb {R}^3$$ 0 ∈ R 3 and eigenvalues $$\pm bi,c$$ ± b i , c with $$b,c\in \mathbb {R}$$ b , c ∈ R and $$b\ne 0$$ b ≠ 0 . We prove that all cycles of $$\xi $$ ξ in a sufficiently small neighborhood of 0, if they exist, are contained in the union of finitely many subanalytic invariant surfaces, each one entirely composed of a continuum of cycles. In particular, we solve Dulac’s problem for such vector fields, i.e., finiteness of limit cycles.

Unconventional spin textures emerging from a universal symmetry theory of spin-momentum locking

Spin textures, i.e., the distribution of spin polarization vectors in reciprocal space, exhibit diverse patterns determined by symmetry constraints, resulting in a variety of spintronic phenomena. Here, we propose a universal theory to comprehensively describe the nature of spin textures by incorporating three symmetry flavors of reciprocal wavevector, atomic orbital, and atomic site. Such an approach enables us to establish a complete classification of spin textures constrained by the little co-group and predict some exotic spin texture types, such as Zeeman-type spin splitting in antiferromagnets and quadratic spin texture. To illustrate the influence of atomic orbitals and sites on spin textures, we predict orbital-dependent spin texture and anisotropic spin-momentum-site locking effects, and corresponding material candidates validated through first-principles calculations. The comprehensive classification and the predicted new spin textures in realistic materials are expected to trigger future spin-based functionalities in electronics.

Fast mobility analysis for generative design applications through a real vector space representation of mobilities

During the early stages of design, mechanisms are commonly modeled as perfect joints assembled with infinitely rigid bodies. This representation enables the prediction of the system’s mobilities through a mobility analysis. However, traditional mobility analysis tools can be computationally expensive or lack critical information, such as the type or direction of mobilities. It hinders the generation of topology and configuration through generative design schemes.In this paper, we propose an alternative approach to mobility analysis based on a real vector space representation of mobilities. Our method provides relevant information for early design steps while being computationally effective through a novel formulation of series and parallel assembly topological operations. A benchmark on four selected use cases highlights an acceleration of 3 to 4 orders of magnitude compared to traditional approaches. Additionally, design rules on the joints’ positions can be automatically generated with our approach. It enables the automation of the complete design process, including topology and configuration. As such, we provide guidelines to develop a generative design scheme dedicated to the synthesis of guiding mechanisms.

Quaternion Nuclear Norm Minus Frobenius Norm Minimization for color image reconstruction

Color image restoration methods typically represent images as vectors in Euclidean space or combinations of three monochrome channels. However, they often overlook the correlation between these channels, leading to color distortion and artifacts in the reconstructed image. To address this, we present Quaternion Nuclear Norm Minus Frobenius Norm Minimization (QNMF), a novel approach for color image reconstruction. QNMF utilizes quaternion algebra to capture the relationships among RGB channels comprehensively. By employing a regularization technique that involves nuclear norm minus Frobenius norm, QNMF approximates the underlying low-rank structure of quaternion-encoded color images. Theoretical proofs are provided to ensure the method’s mathematical integrity. Demonstrating versatility and efficacy, the QNMF regularizer excels in various color low-level vision tasks, including denoising, deblurring, inpainting, and random impulse noise removal, achieving state-of-the-art results.