Search Results (159)

In the evolving digital landscape, the pervasive influence of artificial intelligence (AI) on social media platforms reveals a compelling paradox: the capability to provide personalized experiences juxtaposed with inherent biases reminiscent of human imperfections. Such biases prompt rigorous contemplation on matters of fairness, equity, and societal ramifications, and penetrate the foundational essence of AI. Within this intricate context, the present work ventures into novel domains by examining the potential of quantum computing as a viable remedy for bias in artificial intelligence. The conceptual framework of the quantum sentinel is presented—an innovative approach that employs quantum principles for the detection and scrutiny of biases in AI algorithms. Furthermore, the study poses and investigates the question of whether the integration of advanced quantum computing to address AI bias is seen as an excessive measure or a requisite advancement commensurate with the intricacy of the issue. By intertwining quantum mechanics, AI bias, and the philosophical considerations they induce, this research fosters a discourse on the journey toward ethical AI, thus establishing a foundation for an ethically conscious and balanced digital environment. We also show that the quantum Zeno effect can protect SVM hyperplanes from bias through targeted simulations. Full article

With the increasing penetration of distributed generation (DG), integrated main-distribution networks (IMDNs) face challenges in rapidly and effectively performing comprehensive operational risk assessments under multiple uncertainties. Thereby, using the traditional hierarchical economic scheduling method makes it difficult to accurately find the optimal scheduling operating point. To address this problem, this paper proposes a multi-objective dispatch decision-making optimization model for the IMDN with static security region (SSR) constraints. Firstly, the non-sequential Monte Carlo sampling is employed to generate diverse operational scenarios, and then the key risk characteristics are extracted to construct the risk assessment index system for the transmission and distribution grid, respectively. Secondly, a hyperplane model of the SSR is developed for the IMDN based on alternating current power flow equations and line current constraints. Thirdly, a risk assessment matrix is constructed through optimal power flow calculations across multiple load levels, with the index weights determined via principal component analysis (PCA). Subsequently, a scheduling optimization model is formulated to minimize both the system generation costs and the comprehensive risk, where the adaptive grid density-improved multi-objective particle swarm optimization (AG-MOPSO) algorithm is employed to efficiently generate Pareto-optimal operating point solutions. A membership matrix of the solution set is then established using fuzzy comprehensive evaluation to identify the optimal compromised operating point for dispatch decision support. Finally, the effectiveness and superiority of the proposed method are validated using an integrated IEEE 9-bus and IEEE 33-bus test system. Full article

The secret sharing schemes (SSS) are widely used in secure multi-party computing and distributed computing, and the access structure is the key to constructing secret sharing schemes. In this paper, we propose a method for constructing access structures based on hyperplane combinatorial structures over finite fields. According to the given access structure, the corresponding secret sharing scheme that can identify cheaters is given. This scheme enables the secret to be correctly restored if the cheater does not exceed the threshold, and the cheating behavior can be detected and located. Full article

Although machine learning (ML) models are widely used in many fields, their prediction processes are often hard to understand. This lack of transparency makes it harder for people to trust them, especially in high-stakes fields like healthcare and finance. Human-interpretable explanations for model predictions are crucial in these contexts. While existing local interpretation methods have been proposed, many suffer from low local fidelity, instability, and limited effectiveness when applied to highly nonlinear models. This paper presents SVM-X, a model-agnostic local explanation approach designed to address these challenges. By leveraging the inherent symmetry of the SVM hyperplane, SVM-X precisely captures the local decision boundaries of complex nonlinear models, providing more accurate and stable explanations. Experimental evaluations on the UCI Adult dataset, the Bank Marketing dataset, and the Amazon Product Review dataset demonstrate that SVM-X consistently outperforms state-of-the-art methods like LIME and LEMNA. Notably, SVM-X achieves up to a 27.2% improvement in accuracy. Our work introduces a reliable and interpretable framework for understanding machine learning predictions, offering a promising new direction for future research. Full article

Aiming at the limitations of existing multisensor fault diagnosis methods for rolling bearings in real industrial scenarios, this paper proposes an innovative intuitionistic fuzzy weighted least squares twin support higher-order tensor machine (IFW-LSTSHTM) model, which realizes a breakthrough in the noise robustness, adaptability to the working conditions, and the class imbalance processing capability. First, the multimodal feature tensor is constructed: the fourier synchro-squeezed transform is used to convert the multisensor time-domain signals into time–frequency images, and then the tensor is reconstructed to retain the three-dimensional structural information of the sensor coupling relationship and time–frequency features. The nonlinear feature mapping strategy combined with Tucker decomposition effectively maintains the high-order correlation of the feature tensor. Second, the adaptive sample-weighting mechanism is developed: an intuitionistic fuzzy membership score assignment scheme with global–local information fusion is proposed. At the global level, the class contribution is assessed based on the relative position of the samples to the classification boundary; at the local level, the topological structural features of the sample distribution are captured by K-nearest neighbor analysis; this mechanism significantly improves the recognition of noisy samples and the handling of class-imbalanced data. Finally, a dual hyperplane classifier is constructed in tensor space: a structural risk regularization term is introduced to enhance the model generalization ability and a dynamic penalty factor is set to set adaptive weights for different categories. A linear equation system solving strategy is adopted: the nonparallel hyperplane optimization is converted into matrix operations to improve the computational efficiency. The extensive experimental results on the two rolling bearing datasets have verified that the proposed method outperforms existing solutions in diagnostic accuracy and stability. Full article

This paper considers some innovative theoretical features and practical applications of the normal system of equations used for estimating parameters in multiple linear regression. The Laplace expansion of a determinant by cofactors and double Laplace expansion are employed for resolving the normal system. Additional features are described, including the ridge regularization applied directly to the normal system, geometric interpretation as a unique hyperplane through the points of special weighted means, Mahalanobis distances from observations to these means for the linear link functions, and multidimensional interpolation. The found properties are useful for a better understanding and interpretation of multiple regression, and the numerical examples demonstrate convenience and applicability of these tools in data modeling. Full article

Cross parity codes are mostly used as 2-dimensional codes, and sometimes as 3-dimensional codes. We argue that higher dimensions can help to reduce the number of parity bits, and thus deserve further investigation. As a start, we investigate parities from $(d-2)$-dimensional hyperplanes in d-dimensional parity codes, instead of parities from $(d-1)$-dimensional hyperplanes as usual. Full article

Detecting hate speech in social media is challenging due to its rarity, high-dimensional complexity, and implicit expression via sarcasm or spelling variations, rendering linear models ineffective. In this study, the SVM (Support Vector Machine) algorithm is used to map text features from low-dimensional to high-dimensional space using kernel function techniques to meet complex nonlinear classification challenges. By maximizing the category interval to locate the optimal hyperplane and combining nuclear techniques to implicitly adjust the data distribution, the classification accuracy of hate speech detection is significantly improved. Data collection leverages social media APIs (Application Programming Interface) and customized crawlers with OAuth2.0 authentication and keyword filtering, ensuring relevance. Regular expressions validate data integrity, followed by preprocessing steps such as denoising, stop-word removal, and spelling correction. Word embeddings are generated using Word2Vec’s Skip-gram model, combined with TF-IDF (Term Frequency–Inverse Document Frequency) weighting to capture contextual semantics. A multi-level feature extraction framework integrates sentiment analysis via lexicon-based methods and BERT for advanced sentiment recognition. Experimental evaluations on two datasets demonstrate the SVM model’s effectiveness, achieving accuracies of 90.42% and 92.84%, recall rates of 88.06% and 90.79%, and average inference times of 3.71 ms and 2.96 ms. These results highlight the model’s ability to detect implicit hate speech accurately and efficiently, supporting real-time monitoring. This research contributes to creating a safer online environment by advancing hate speech detection methodologies. Full article

This study investigates the singularity structures of lightlike hypersurfaces generated by null Cartan curves in Minkowski spacetime. We construct a hierarchical geometric framework consisting of a lightlike hypersurface $L{H}_{\mathit{\beta }}$, a critical lightlike surface $L{S}_{\mathit{\beta }}$, and a degenerate curve $L{C}_{\mathit{\beta }}$, with dimensions decreasing from 3D to 1D. Using singularity theory, we identify a novel geometric invariant $\sigma \left(t\right)$ that governs the emergence of specific singularity types, including $C(2,3)\times {\mathbb{R}}^2$, $SW\times \mathbb{R}$, $BF$, $C\left(BF\right)$, $C(2,3,4)\times \mathbb{R}$, and $(2,3,4,5)$-cusp. These singularities exhibit increasing degeneracy as the hierarchy progresses, with contact orders between the lightlike hyperplane $H{S}_{t_0}^L$ and the curve $\mathit{\beta }$ systematically intensifying. An explicit example demonstrates the construction of these objects and validates the theoretical results. This work establishes a systematic connection between null Cartan curves, stratified singularities, and contact geometry. Full article

This paper presents a method for dynamic pattern recognition and classification of one dangerous caterpillar species to allow for its control in maize crops. The use of dynamic pattern recognition supports the identification of patterns in digital image data that change over time. In fact, identifying fall armyworms (Spodoptera frugiperda) is critical in maize production, i.e., in all of its growth stages. For such pest control, traditional agricultural practices are still dependent on human visual effort, resulting in significant losses and negative impacts on maize production, food security, and the economy. Such a developed method is based on the integration of digital image processing, multivariate statistics, and machine learning techniques. We used a supervised machine learning algorithm that classifies data by finding an optimal hyperplane that maximizes the distance between each class of caterpillar with different lengths in N-dimensional spaces. Results show the method’s efficiency, effectiveness, and suitability to support decision making for this customized control context. Full article

This study explores a unique Finsler space with a Rander’s-type exponential metric, $\mathcal{G}(\alpha ,\beta )=(\alpha +\beta )e^{{\displaystyle \frac{\beta }{(\alpha +\beta )}}}$, where $\alpha$ is a Riemannian metric and $\beta$ is a 1-form. We analyze the conditions under which its hypersurfaces behave like hyperplanes of the first, second, and third kinds. Additionally, we examine the reducibility of the Cartan tensor $\mathcal{C}$ for these hypersurfaces, providing insights into their geometric structure. Full article

Let $X\subset {\mathbb{P}}^n$, where $3\le n\le 5$, be an irreducible hypersurface of degree $d\ge 2$. Fix an integer $t\ge 3$. If $n=5$, assume $t\ge 4$ and $(t,d)\ne (4,2)$. Using the Differential Horace Lemma, we prove that ${\mathcal{O}}_X\left(t\right)$ is not secant defective. For a fixed X, our proof uses induction on the integer t. The key points of our method are that for a fixed X, we only need the case of general linear hyperplane sections of X in lower-dimension projective spaces and that we do not use induction on d, allowing an interested reader to tackle a specific X for $n>5$. We discuss (as open questions) possible extensions of some weaker forms of the theorem to the case where $n>5$. Full article

Traditional fault diagnosis methods often require extracting features from raw vibration signals based on prior knowledge, which are then input into intelligent classifiers for pattern recognition. This process is prone to information loss and can be inaccurate when relying on human experience for fault identification. To address this issue, this paper proposes an intelligent fault classification and diagnosis model for rolling bearings based on Fast Fourier Transform (FFT) combined with a time convolutional network (SE-TCN) incorporating an attention mechanism, with a Support Vector Machine (SVM) used as the classifier. First, the FFT is applied to transform the collected raw time-domain data of bearing faults into the frequency domain, obtaining the sequence information in the frequency domain. Second, the frequency–domain sequence data are fed into the SE-TCN model, which uses multiple convolutional layers and a channel attention mechanism to extract deep fault features. Finally, the extracted feature vectors are input into the SVM classifier, and the Particle Swarm Optimization (PSO) algorithm is used to optimize the SVM parameters. The optimal separating hyperplane is obtained through training to classify the fault types of the rolling bearings. To verify the effectiveness and diagnostic performance of the proposed method, experiments are conducted using bearing fault datasets from Case Western Reserve University (CWRU) and a laboratory self-built fault diagnosis experimental platform. The experimental results show that the classification accuracy of the proposed method exceeds 99% on the CWRU test dataset, and it also demonstrates advantages in handling small sample data, with an accuracy of over 90%. Additionally, it exhibits good diagnostic performance on the bearing fault data collected from the laboratory self-built platform. The results validate the effectiveness of the proposed classification model in bearing a fault diagnosis. Full article

This article considers a class of entire functions of several complex variables that are bounded in the Cartesian product of some half-planes. Each such hyperplane is defined on the condition that the real part of the corresponding variable is less than some r. For this class of functions, there are established analogs of the Wiman theorems. The first result describes the behavior of an entire function from the given class at the neighborhood of the point of the supremum of its modulus. The second result shows asymptotic equality for supremums of the modulus of the function and its real part outside some exceptional set. In addition, the analogs of Wiman’s theorem are obtained for entire multiple Dirichlet series with arbitrary non-negative exponents. These results are obtained as consequences of a new statement describing the behavior of an entire function $F\left(z\right)$ of several complex variables $z=(z_1,\dots ,z_p)$ at the neighborhood of a point w, where the value $F\left(w\right)$ is close to the supremum of its modulus on the boundary of polylinear domains. The paper has two moments of novelty: the results use a more general geometric exhaustion of p-dimensional complex space by polylinear domains than previously known; another aspect of novelty concerns the results obtained for entire multiple Dirichlet series. There is no restriction that every component of exponents is strictly increasing. These statements are valid for any non-negative exponents. Full article

Deep connectionist models are characterized by many neurons grouped together in many successive layers. As a result, their data classifications are difficult to understand. We present two novel algorithms which explain the responses of several black-box machine learning models. The first is Fidex, which is local and thus applied to a single sample. The second, called FidexGlo, is global and uses Fidex. Both algorithms generate explanations by means of propositional rules. In our framework, the discriminative boundaries are parallel to the input variables and their location is precisely determined. Fidex is a heuristic algorithm that, at each step, establishes where the best hyperplane is that has increased fidelity the most. The algorithmic complexity of Fidex is proportional to the maximum number of steps, the number of possible hyperplanes, which is finite, and the number of samples. We first used FidexGlo with ensembles and support vector machines (SVMs) to show that its performance on three benchmark problems is competitive in terms of complexity, fidelity and accuracy. The most challenging part was then to apply it to convolutional neural networks. We achieved this with three classification problems based on images. We obtained accurate results and described the characteristics of the rules generated, as well as several examples of explanations illustrated with their corresponding images. To the best of our knowledge, this is one of the few works showing a global rule extraction technique applied to both ensembles, SVMs and deep neural networks. Full article