As cyberattacks become more advanced, advanced AI-based big data visualization is now needed for effective threat detection. Yet, choosing the best visualization tools is some multicriteria decision-making (MCDM) task that involves considering many criteria containing both positive and negative aspects. WhileMCDMmethods that address the selection and classification of AI-driven big data visualization tools focus on the positive aspects of the evaluation criteria and ignore the negative aspects of the criteria, resulting in incomplete evaluations. Further, although Einstein operators have shown strong results in uncertain and imprecise situations and MCDM approaches, they have not yet been used in bipolar fuzzy frameworks, which leaves a major gap in decision-making methods. To overcome these problems, this article interprets a bipolar fuzzy MCDM methodology based on Einstein prioritized operators to systematically evaluate and classify AI-driven big data visualization tools for cybersecurity threat detection. For this method, Einstein prioritized operators within a bipolar fuzzy framework devised in this article, which can aggregate both positive and negative aspects of the criteria.Acomprehensive case study is shown to assess and classify the prominent AI-driven big data visualization tools for cybersecurity threat detection, considering critical criteria with dual aspects. The proposed methodology is meticulously compared with the prevailing MCDM methods to validate its dominance in handling uncertainty and the bipolarity of the criteria. This article helps security professionals choose the right AI-powered visualization tools which, in turn improve the cybersecurity of their organizations and make it easier to detect threats.

The invariant properties of the stability, reachability, observability and transfer matrices of positive linear continuous-time systems with integer and fractional orders are investigated. It is shown that the stability, reachability, observability and transfer matrix of positive linear systems are invariant under their integer and fractional orders.

This paper presents a novel computational framework for assessing cardiovascular disease (CVD) risk by integrating unsupervised clustering techniques with survival analysis. The proposed method enables dynamic and individualized risk prediction by organizing patient data into structured clusters based on shared cardiovascular risk factors. The framework begins with competitive learning, an unsupervised clustering method, to group patients into clusters that reflect distinct risk profiles. Each cluster is represented by its centroid, calculated as the mean of the 9-dimensional feature vectors of its members, ensuring that the clusters effectively summarize patient data while preserving critical risk characteristics. For each cluster, an independent Cox Proportional Hazards Model is applied to analyze survival data, capturing the unique relationships between cardiovascular risk factors and survival outcomes within that cluster. A key innovation of this study is the introduction of the Cumulative Prevalence Ratio (CPR), a new metric that aggregates hazard rates over time separately for each cluster. This approach provides a comprehensive view of cumulative cardiovascular risk, enabling precise categorization of the patient into risk groups based on cumulative exposure to evolving risk factors. By integrating cluster-specific hazard functions and temporal risk metrics, the proposed framework improves the precision and adaptability of CVD risk predictions, paving the way for personalized and data-driven healthcare interventions.

This article addresses modeling systems using fractional order derivatives, highlighting three basic approaches: differential equations, operator methods, and state space representations. Each approach carries different advantages and limitations in the context of time invariant linear systems (LTI) of fractional order. The focus of the article is on Fractional Order Transfer Functions, which represent a special subject of interest because they offer practical utility with available simulation libraries (e.g., CRONE, FOMCON, NiNteger) and approximation techniques (e.g., Oustaloup, CFE, Thiele, Padé). This paper describes a transition between fractional order transfer functions (FOTF) and pseudo-rational representations of such systems. While the existing literature contains the basics of fractional differential equations and operator theory, it often omits explicit formulas for conversion between different representations. The paper fills a significant gap by proposing a novel algorithm for converting FOTF models to fractional LTI representations. Unlike previous works that implicitly assume such transitions exist, this paper provides formulas for coefficient transformations and demonstrates its effectiveness by minimizing the degree of the system.

The emergence of Game theory (GT) enabled with demand side management (DSM) has the applications in the field of smart grid applications. A mathematical method called game theory uses desirable rules to identify the circumstances under which all actors can win. Various agents can be used to optimize their gains. In terms of customer utility, demand response algorithms are categorized as agents in terms of customer utility. A centralized demand response (DR) scheduling algorithm that meets the varied energy consumption needs of a community can be difficult owing to the differences among residents. A non-cooperative DR-GT model is proposed to improve individual benefits in the energy consumption scheduling algorithm. The appliance information comprises different power levels to categorize the residents, which reduces the scheduling traffic between the residents and aggregator. There is a 23% reduction in the peak-to average ratio and increase in renewable energy usage by 13–25%, as better scheduling based on the flexibility of consumer loads and pricing schemes. Smart grid efficiency is improved by 23–30%, owing to reduced energy losses, fewer system imbalances, and lower wears on grid infrastructure.

The aim of this paper is to analyze the development of algorithms for Fast Matrix Multiplication (FMM) in both historical and technical contexts, as well as to compare available solutions on consumer-grade computer hardware. We review advancements in estimating the theoretical computational complexity of FMM and optimization techniques that are used in widely adopted algorithms, with a particular focus on optimal cache memory usage and leveraging Graphics Processing Units (GPU). The methodology of tests and their analysis highlight the performance differences of the considered algorithms depending on the matrix size and the nature of the data stored in them. Results indicate the significant role of tailoring the chosen algorithm to the available hardware and the specific application in which the algorithm is being performed. Also, we emphasize that the FMM algorithms can be applied not only to linear algebra problems but also to current problems in science and engineering, such as artificial intelligence, databases, parallel computations, computational biology, pattern recognition, and compiler construction, to mention just a few examples.

In this research work, we first obtain a new 3-D chaotic Lü system by modifying the dynamics of the classical Lü chaotic system (2002). Next, by introducing a state feedback to the new 3-D modified Lü chaotic system, we obtain a new 4-D hyperchaotic Lü system with a curve equilibrium.We carry out a detailed bifurcation analysis of the new4-D hyperchaotic system with a curve equilibrium and describe the bifurcation transition diagrams and Lyapunov exponents diagrams.We also derive new multistability results of the new 4-D hyperchaotic Lü system with a curve equilibrium. For engineering applications, we provide an electronic circuit simulation of the proposed hyperchaotic Lü system using MultiSim 14.0. As a control application, we derive new results for the complete synchronization for a pair of new hyperchaotic Lü systems taken as the master and slave systems. We have used integral sliding mode control for the derivation of the synchronizing control law for the complete synchronization design for the new hyperchaotic Lü system. MATLAB simulations are provided to illustrate the main results of this research work.

This work presents a reinforcement learning framework for controlling a planar threesection continuum robot in environments with static obstacles. Assuming constant curvature for each section, the robot is trained to navigate toward a fixed goal while avoiding collisions with multiple static objects. A custom simulation environment was developed to support three levels of scenario difficulty, easy, medium and hard, each with varying obstacle density and placement. The learning process is driven by the Deep Deterministic Policy Gradient (DDPG) algorithm, which enables smooth and continuous curvature control. Careful attention was paid to the design of the reward function and the network architecture, both of which were critical to achieving stable and reliable policy learning. Performance was evaluated across multiple runs, revealing that the agent successfully generalized its behavior across scenarios of increasing complexity. The proposed framework demonstrates the potential of reinforcement learning as a viable approach to safe and adaptive control in continuum robotic systems, with promising implications for applications such as medical navigation, search and rescue, and inspection in confined environments.

In this paper, we provide some sufficient conditions for the exponential stability of solutions of nonlinear impulsive differential systems by using some inequality of Gronwall-Bellman type. Practical exponential stability is also investigated for a class of perturbed impulsive systems. Several numerical examples are provided to demonstrate the effectiveness of the theoretical results. Furthermore, Hopfield neural networks system is discussed as an application.

Linear and mixed binary programming techniques, which arise from model linearity, are widely supported by advanced optimization solvers. In this paper, we present a comprehensive guide for transforming linear classifiers into linear or mixed binary programming tasks. Our approach employs widely used techniques, such as Kesler construction with either perfect or imperfect learning, and weight regularization using the L1 or L0 norm, enhanced by additional maximum weight constraint (i.e., L∞). Various linear optimization tasks are formulated based on performance measures such as accuracy and sensitivity. The classifiers are constructed using different weight penalizations and regularizations – specifically, the L0 norm, which yields mixed binary programming tasks with NP-hard complexity, and the L1 norm, which results in linear programming tasks with polynomial complexity, both with an additional maximum weight constraint. The proposed classifiers are compared on several UCI datasets (Iris Flower, Wine, and Seeds) and match or outperform Ridge and Lasso regression methods when applied to classification tasks.