This paper proposes an intelligent load balancing framework for distributed big data processing systems that integrates machine learning techniques with adaptive weight-based decision mechanisms. The study addresses limitations of traditional static load balancing methods, which do not account for dynamic workload variations and heterogeneous request characteristics, leading to inefficient resource utilization and bottlenecks in multi-node environments. The proposed approach combines an online learning model for real-time estimation of request complexity with multi-parameter evaluation of node states, including CPU utilization, memory consumption, queue length, response latency, and cache efficiency. A dynamic weighting strategy is used to construct an integrated load indicator for adaptive request distribution across nodes. The framework is deployed within a multi-layer distributed architecture consisting of clustered application servers, distributed databases, caching subsystems, and monitoring components, ensuring scalable and fault-tolerant processing. For evaluation, a three-node simulation environment was used with 10,000 heterogeneous requests, followed by extended testing on semi-realistic workload traces derived from web traffic patterns and database query logs. The dataset included over 1.2 million requests, capturing bursty arrivals, skewed distributions, and heterogeneous complexity. Experimental results show that the proposed method improves load distribution uniformity to 6%, reduces average response time to 210 ms, and increases throughput up to 13,800 requests per second. Statistical validation using confidence intervals and hypothesis testing confirms a 47% (±3.2% at 95% confidence level) reduction in mean response time and throughput improvement up to 14,200 requests per second under realistic workloads. 

This paper presents a set of feature selection methods for intelligent software performance monitoring based on machine learning models, with a focus on improving interpretability, scalability, and adaptability in high-dimensional telemetry analysis. The research addresses limitations of traditional statistical and rule-based approaches, which are often unable to capture nonlinear dependencies and dynamic interactions in modern distributed architectures. A unified methodology is proposed that integrates several complementary techniques for adaptive feature selection in intelligent monitoring systems. These include a topology-aware method based on graph neural networks for modeling structural dependencies in microservice architectures, a correlation-driven approach for reducing feature redundancy, a multifactor fusion method combining statistical significance, temporal stability, and predictive contribution, a cost-efficient strategy for serverless environments, and a context-aware reinforcement learning approach for dynamic feature adaptation. The proposed methods are evaluated on a large-scale dataset exceeding 3.5 TB, collected from 42 real-world applications representing monolithic, microservice, cloud-native, and serverless architectures. The results show an average reduction in feature dimensionality of 37%, while maintaining over 95% predictive accuracy across multiple models. Additional improvements include, on average, a 21% increase in dependency modeling accuracy, an 18% gain in feature relevance estimation, a 26% reduction in feature instability under dynamic workloads, and up to 42% cost reduction in serverless environments, as observed across repeated experiments under controlled workload variability and consistent evaluation settings. While the results demonstrate the effectiveness of adaptive feature selection, further validation in diverse real-world conditions is required to confirm the generalizability of the proposed framework.

This article introduces a novel variational approach for solving the inverse geodesic problem on a transcendental surface shaped as a cylindrical structure with a cycloidal generatrix, a type of geometry that has not been previously studied in this context. Unlike classical models that rely on symmetric surfaces such as spheres or spheroids, this method formulates the geodesic path as a functional minimization problem. By applying the Euler–Lagrange equation, an analytical integration of the corresponding second-order differential equation is achieved, resulting in a parametric expression that satisfies boundary conditions. The effectiveness of the proposed method for computing geodesic curves on transcendental surfaces has been rigorously evaluated through a series of numerical experiments. Analytical validation has been carried out using MathCad, while simulation and three-dimensional visualization have been implemented in Python. Numerical experiments are conducted and 3D visualizations of the geodesic lines are presented for multiple point pairs on the surface, demonstrating the accuracy and computational efficiency of the proposed solution. This enables a closed-form analytical representation of the geodesic curve, significantly reducing computational complexity compared to existing numerical-heuristic methods.
The obtained results offer clear advantages over existing studies in the field of computational geometry and variational calculus. Specifically, the proposed method enables the construction of geodesic curves on complex transcendental surfaces where traditional methods either fail or require intensive numerical approximation. 
The analytical integration of geodesic equations enhances both accuracy and performance, achieving an average computational cost reduction of approximately 27-30% and accuracy improvement of around 20% in comparison with previous models utilizing non-polynomial metrics. These enhancements are especially relevant in applications requiring real-time response and precision, such as robotics, CAD systems, computer graphics, and virtual environment simulation. The method’s ability to deliver compact and exact solutions for boundary value problems positions it as a valuable contribution for both theoretical and applied sciences.

Dynamic behavior of a heavy homogeneous sphere in a spherical cavity of a supporting body that performs specified translational movements in space has been studied. Using the Appel formalism, the equations of ball motion in a moving spherical cavity without slip are constructed and a numerical analysis of the evolution of the ball motion is carried out.