Vector Space Research Articles

Guided Diverse Concept Miner (GDCM): Uncovering Relevant Constructs for Managerial Insights from Text

The Guided Diverse Concept Miner (GDCM) is an innovative deep learning algorithm tailored for the extraction of managerially relevant concepts from textual data, emphasizing the autonomy in discovering insights without predefined labels or guidance. This tool stands out by embedding words, documents, and concepts within the same vector space, which simplifies the interpretation of unearthed concepts and ensures their alignment with managerial outcomes. Central to GDCM’s methodology is its capacity to focus on concepts that are highly correlated with user-specified managerial outcomes, termed guiding variables, thereby enhancing the relevance and application of extracted insights in decision-making processes. The algorithm’s design inherently promotes the diversity of the recovered concepts, ensuring a broad spectrum of insights. Through practical application in analyzing customer reviews related to online purchases, GDCM not only identified key concepts influencing conversion rates but also validated its findings against established theories and prior causal research. This validation underscores GDCM’s utility in generating actionable, diverse insights tailored to specific managerial contexts, marking a significant advancement in how businesses leverage textual data for strategic decisions.

On the running and the UV limit of Wilsonian renormalization group flows

Abstract In nonperturbative formulation of quantum field theory (QFT), the vacuum state is characterized by the Wilsonian renormalization group (RG) flow of Feynman type field correlators. Such a flow is a parametric family of ultraviolet (UV) regularized field correlators, the parameter being the strength of the UV regularization, and the instances with different strength of UV regularizations are linked by the renormalization group equation (RGE). Important RG flows are those which reach out to any UV regularization strengths. In this paper it is shown that for these flows a natural, mathematically rigorous generally covariant definition can be given, and that they form a topological vector space which is Hausdorff, locally convex, complete, nuclear, semi-Montel, Schwartz. That is, they form a generalized function space having favorable properties, similar to multivariate distributions. The other theorem proved in the paper is that for Wilsonian RG flows reaching out to all UV regularization strengths, a simple factorization formula holds in case of bosonic fields over flat (affine) spacetime: the flow always originates from a regularization-independent distributional correlator, and its running satisfies an algebraic ansatz. The conjecture is that this factorization theorem should generically hold, which is worth future investigations.

On some pre-orders and partial orders of linear operators on infinite dimensional vector spaces

AbstractThis article is devoted to the generalization of the Drazin pre-order and the G-Drazin partial order to Core-Nilpotent endomorphisms over arbitrary k-vector spaces, namely, infinite dimensional ones. The main properties of this orders are described, such as their respective characterizations and the relations between these orders and other existing ones, generalizing the existing theory for finite matrices. In order to do so, G-Drazin inverses are also studied in this framework. Also, it includes a generalization of the space pre-order to linear operators over arbitrary k-vector spaces.

Enhancing Knowledge Graph Embedding with Hierarchical Self-Attention and Graph Neural Network Techniques for Drug-Drug Interaction Prediction in Virtual Reality Environments

In biomedicine, the critical task is to decode Drug–Drug Interactions (DDIs) from complex biomedical texts. The scientific community employs Knowledge Graph Embedding (KGE) methods, enhanced with advanced neural network technologies, including capsule networks. However, existing methodologies primarily focus on the structural details of individual entities or relations within Biomedical Knowledge Graphs (BioKGs), overlooking the overall structural context of BioKGs, molecular structures, positional features of drug pairs, and their critical Relational Mapping Properties. To tackle the challenges identified, this study presents HSTrHouse an innovative hierarchical self-attention BioKGs embedding framework. This architecture integrates self-attention mechanisms with advanced neural network technologies, including Convolutional Neural Network (CNN) and Graph Neural Network (GNN), for enhanced computational modeling in biomedical contexts. The model bifurcates the BioKGs into entity and relation layers for structural analysis. It employs self-attention across these layers, utilizing PubMedBERT and CNN for position feature extraction, and a GNN for drug pair molecular structure analysis. Then, we connect the position and molecular structure features to integrate them into the self-attention calculation of entity and relation. After that, the output of the self-attention layer is combined with the connected vectors of the position feature and molecular structure feature to obtain the final representation vector, and finally, to model the Relational Mapping Properties (RMPs), the representation vector is embedded into the complex vector space using Householder projections to obtain the BioKGs model. The paper validates HSTrHouse’s efficacy by comparing it with advanced models on three standard BioKGs for DDIs research.

Vector Equilibrium Problems—A Unified Approach and Applications

We present existing results and properties for the solutions of some vector equilibrium problems with set-valued functions in the case of a vector space ordered by a cone with some “interiority” properties. Some applications concerning the existence of equilibrium for abstract economies and vector optimization problems are given.

Möbius function of the subgroup lattice of a finite group and Euler characteristic

AbstractThe Möbius function of the subgroup lattice of a finite group has been introduced by Hall and applied to investigate several questions. In this paper, we consider the Möbius function defined on an order ideal related to the lattice of the subgroups of an irreducible subgroup G of the general linear group $$\textrm{GL}(n,q)$$ GL ( n , q ) acting on the n-dimensional vector space $$V=\mathbb {F}_q^n$$ V = F q n , where $$\mathbb {F}_q$$ F q is the finite field with q elements. We find a relation between this function and the Euler characteristic of two simplicial complexes $$\Delta _1$$ Δ 1 and $$\Delta _2$$ Δ 2 , the former raising from the lattice of the subspaces of V, the latter from the subgroup lattice of G.

Fast and efficient context-aware embedding generation using fuzzy hashing for in-vehicle network intrusion detection

In the rapidly advancing field of automotive cybersecurity, the protection of In-Vehicle Networks (IVNs) against cyber threats is crucial. Current deep learning solutions offer robustness but at the cost of high computational demand and potential privacy breaches due to the extensive IVN data required for model training. Our study proposes a novel intrusion detection system (IDS) specifically designed for IVNs that prioritizes computational efficiency and data privacy. Utilizing fuzzy hashing techniques, we generate context-aware embeddings that effectively preserve the privacy of IVN data. Among the machine learning algorithms evaluated, the Support Vector Machine (SVM) emerged as the most effective, particularly when paired with TLSH hash embeddings. This combination achieved notable detection performance, as substantiated by T-SNE visualizations that demonstrate a distinct segregation of normal and attack traffic within the vector space. To validate the effectiveness and practicality of our proposed IDS, we conducted exhaustive experiments on the well-known car-hacking dataset and the more complex ROAD dataset, which includes diverse and sophisticated attack scenarios. Our findings reveal that the proposed lightweight IDS not only demonstrates high detection accuracy but also maintains this performance within the computational constraints of current IVN systems. The system's capability to operate effectively in real-time environments makes it a viable solution for modern automotive cybersecurity needs.

Invariant Grassmannians and a K3 surface with an action of order 192*2

Given a complex vector space V of finite dimension, its Grassmannian variety parametrizes all subspaces of V of a given dimension. Similarly, if a finite group G acts on V, its invariant Grassmannian parametrizes all the G−invariant subspaces of V of a given dimension. Based on this fact, we develop an algorithm for finding equations of G−invariant projective varieties arising as an intersection of hypersurfaces of the same degree.We apply the algorithm to find equations describing a polarized K3 surface with a faithful action of T192⋊μ2 and some further symmetric K3 surfaces with a degree 8 polarization.

From vector spaces to DRM lists: False Memory Generator, a software for automated generation of lists of stimuli inducing false memories.

The formation of false memories is one of the most widely studied topics in cognitive psychology. The Deese-Roediger-McDermott (DRM) paradigm is a powerful tool for investigating false memories and revealing the cognitive mechanisms subserving their formation. In this task, participants first memorize a list of words (encoding phase) and next have to indicate whether words presented in a new list were part of the initially memorized one (recognition phase). By employing DRM lists optimized to investigate semantic effects, previous studies highlighted a crucial role of semantic processes in false memory generation, showing that new words semantically related to the studied ones tend to be more erroneously recognized (compared to new words less semantically related). Despite the strengths of the DRM task, this paradigm faces a major limitation in list construction due to its reliance on human-based association norms, posing both practical and theoretical concerns. To address these issues, we developed the False Memory Generator (FMG), an automated and data-driven tool for generating DRM lists, which exploits similarity relationships between items populating a vector space. Here, we present FMG and demonstrate the validity of the lists generated in successfully replicating well-known semantic effects on false memory production. FMG potentially has broad applications by allowing for testing false memory production in domains that go well beyond the current possibilities, as it can be in principle applied to any vector space encoding properties related to word referents (e.g., lexical, orthographic, phonological, sensory, affective, etc.) or other type of stimuli (e.g., images, sounds, etc.).

Preferences, risk neutrality and risk-sensitive MDPs

Preferences, risk neutrality and risk-sensitive MDPs

Binary convex fuzzy vector spaces over binary vector spaces and their applications

Binary convex fuzzy vector spaces over binary vector spaces and their applications

VCGERG

Vulnerability can lead to data loss, privacy leakage and financial loss. Accurate detection and identification of vulnerabilities is essential to prevent information leakage and APT attacks. This paper explores the possibility of digging the valuable information in vulnerability reports deeply. We propose a new model, VCGERG, which products a graph using key information from vulnerability reports and embeds the graph into the vector space using a keywords-LINE graph embedding algorithm based on the attention of neighboring nodes. VCGERG model uses the OVR random forest algorithm to classify vulnerabilities. Our model can get the complicated local and global information of the graph in large-scale dataset and achieve better results. In order to verify the effectiveness of our model, it is evaluated on many experiments. Compared with other models, our method has a higher accuracy rate of 0.975.

The theory of screws derived from a module over the dual numbers

AbstractThe theory of screws clarifies many analogies between apparently unrelated notions in mechanics, including the duality between forces and angular velocities. It is known that the real 6-dimensional space of screws can be endowed with an operator $$\mathcal {E}$$ E , $$\mathcal {E}^2=0$$ E 2 = 0 , that converts it into a rank 3 free module over the dual numbers. In this paper we prove the converse, namely, given a rank 3 free module over the dual numbers, endowed with orientation and a suitable scalar product ($$\mathbb {D}$$ D -module geometry), we show that it is possible to define, in a canonical way, a Euclidean space so that each element of the module is represented by a screw vector field over it. The new approach has the effectiveness of motor calculus while being independent of any reduction point. It gives insights into the transference principle by showing that affine space geometry is basically vector space geometry over the dual numbers. The main results of screw theory are then recovered by using this point of view.

Research and Development of Digital Work Ticket Information Sharing System Based on Mathematical Differential Improved Vector Space Model

In the traditional production business operation and maintenance maintenance involves the work ticket filled by hand, easy to produce errors, and need to review, approval and other operations, low efficiency. The author proposes a digital work ticket sharing system based on mathematical differential improved vector space model, through the integration with PMS2.0 system and security risk management and control platform, achieve mobile office management away from WEB, in terms of functions, it realizes all the functions of the work ticket module in the PMS2.0 system, and integrates various requirements of the on-site paper work ticket, through the application of digital work ticket, real-time data collection and comprehensive sharing of the whole process and business of work ticket are realized, at the same time, according to the requirements of security management and control, data fusion with the security risk management and control platform is realized to improve work efficiency and security sharing.

Spatial Varying Vectorial Holography and Polarization Encryption Based on Birefringent Metasurface

AbstractVectorial holography technology plays a fundamental role by exploring the vectorial nature of light and enriches disruptive applications in optical encryption, display, and manipulation. With its flexible control methods and high‐precision subwavelength design, metasurface possesses rich modulation flexibility that surpasses traditional optical modulation devices. Here, a vectorial holographic design is implemented that can cover various polarization information by using a birefringent metasurface. The design adopts a gradient descent optimization method to jointly optimize the phase information of the orthogonal polarization channels with the birefringent metasurface, for continuous variation of polarization information in the entire vector space on the Poincare Sphere with efficient information integration. Based on the detailed depiction of full vector space polarization texture, such efficient vectorial holographic optimization methods can expand the encryption channels and achieve high spatial resolution allowing large capacity multiplexing, data storage, pattern recognition, etc.

Simple modules for untwisted affine Lie algebras induced from nilpotent loop subalgebras

We construct large families of simple modules for untwisted affine Lie algebras using induction from one-dimensional modules over nilpotent loop subalgebras. We also show that the vector space of the first self-extensions for these module has uncountable dimension and that generic tensor products of these modules are simple.

A general formulation of reweighted least squares fitting

We present a generalized formulation for reweighted least squares approximations. The goal of this article is twofold: firstly, to prove that the solution of such problem can be expressed as a convex combination of certain interpolants when the solution is sought in any finite-dimensional vector space; secondly, to provide a general strategy to iteratively update the weights according to the approximation error and apply it to the spline fitting problem. In the experiments, we provide numerical examples for the case of polynomials and splines spaces. Subsequently, we evaluate the performance of our fitting scheme for spline curve and surface approximation, including adaptive spline constructions.

A metaplectic perspective of uncertainty principles in the linear canonical transform domain

We derive Heisenberg uncertainty principles for pairs of Linear Canonical Transforms of a given function, by resorting to the fact that these transforms are just metaplectic operators associated with free symplectic matrices. The results obtained synthesize and generalize previous results found in the literature, because they apply to all signals, in arbitrary dimension and any metaplectic operator (which includes Linear Canonical Transforms as particular cases). Moreover, we also obtain a generalization of the Robertson-Schrödinger uncertainty principle for Linear Canonical Transforms. We also propose a new quadratic phase-space distribution, which represents a signal along two intermediate directions in the time-frequency plane. The marginal distributions are always non-negative and permit a simple interpretation in terms of the Radon transform. We also give a geometric interpretation of this quadratic phase-space representation as a Wigner distribution obtained upon Weyl quantization on a non-standard symplectic vector space. Finally, we derive the multidimensional version of the Hardy uncertainty principle for metaplectic operators and the Paley-Wiener theorem for Linear Canonical Transforms.

On Resolvability of Graphs Associated with Vector Spaces

Let be a n-dimensional vector space over the field F with a basis . In this paper, we obtain the resolving parameters like metric dimension and partition dimension of graphs associated with vector space. Also, found the values of metric-locating-domination number, locating-domination number, and bipartite decomposition of kind of graph associated with vector space.

Learning Event Representations for Zero-Shot Detection via Dual-Contrastive Prompting

Zero-shot event detection aims to involve the automatic discovery and classification of new events within unstructured text. Current zero-shot event detection methods have not considered addressing the problem more effectively from the perspective of improving event representations. In this paper, we propose dual-contrastive prompting (COPE) model for learning event representations to address zero-shot event detection, which leverages prompts to assist in generating event embeddings using a pretrained language model, and employs a contrastive fusion approach to capture complex interaction information between trigger representations and sentence embeddings to obtain enhanced event representations. Firstly, we introduce a sample generator to create ordered contrastive sample sequences with varying degrees of similarity for each event instance, aiding the model in better distinguishing different types of events. Secondly, we design two distinct prompts to obtain trigger representations and event sentence embeddings separately. Thirdly, we employ a contrastive fusion module, where trigger representations and event sentence embeddings interactively fuse in vector space to generate the final event representations. Experiments show that our model is more effective than the most advanced methods.