Advances in Systems Science and Applications
Advances in Systems Science and Applications (ASSA) is an international peer-reviewed open-source online academic journal. Its scope covers all major aspects of systems (and processes) analysis, modeling, simulation, and control, ranging from theoretical and methodological developments to a large variety of application areas. Survey articles and innovative results are also welcome. ASSA is aimed at the audience of scientists, engineers and researchers working in the framework of these problems. ASSA should be a platform on which researchers will be able to communicate and discuss both their specialized issues and interdisciplinary problems of systems analysis and its applications in science and industry, including data science, artificial intelligence, material science, manufacturing, transportation, power and energy, ecology, corporate management, public governance, finance, and many others.
International Institute for General Systems Studies, Pennsylvania, USA
Vector Fields with Non-Isolated Singular Points Viewed from the Inside and Outside
We present a brief survey of recent results about vector fields with non-isolated singular points and their applications. One of the most interesting and promising application is connected with quasi-linear differential equations of the second order, including the equation of geodesics in signature varying (pseudo-Riemannian) metrics.
Copyright (c) 2025 Advances in Systems Science and Applications
On Linear Differential Equations on the Torus and Non-Standard Analysis
In this paper, we consider periodic boundary value problems for differential equations whose coefficients are trigonometric polynomials. We construct the spaces of generalized functions, where such problems have solutions. In particular, the solvability space of a periodic analogue of the Mizohata equation is constructed. We build also a periodic analogue and a generalization of the construction of the nonstandard analysis, where infinitely small are not only functions, but also functional spaces. To show that not all constructions on the torus lead to a simplification in compare with the plane, we consider a periodic analogue of the hypoelliptic differential operator and show that its number-theoretic properties are significant. In particular, it turns out that if a polynomial with integer coefficients is irreducible in the rational field, then the corresponding differential operator is hypoelliptic on the torus.
differential operator on the torus, linear differential equation on the torus, Mizohata equation, nonstandard analysis, hypoellipticity
Legendre Transformation and Its Applications
We present the Legendre transformation in a geometric way based on the procedure of the Legendrian lift. This approach allows us to understand some interesting properties of it, in particular, the reason for the appearance of singularities of dual curves. Also we consider application of the Legendre transformation to the Clairaut differential equation. Finally, we say a few words class of contact transformations and present an infinite group of contact transformations different from the Legendre transformation.
Legendre transformation, duality, contact transformation, contact structure, pedal curve, singular point, Clairaut equation
Multiple Capture of Coordinated Evaders in the Linear Group Pursuit Problemwith a Simple Matrix and Phase Restrictions
In finite-dimensional Euclidean space, an analysis is made of the problem of pursuit of two evaders by a group of pursuers, which is described by a system of the form $$ \dot z_{ij} = \alpha z_{ij}+ u_i - v,\ u_i, v \in V. $$ It is assumed that the evaders use the same control and do not move out of a convex polyhedral set. The pursuers use counterstrategies based on information about the initial positions and the prehistory of the evaders' control. The set of admissible controls $V$ is a sphere of unit radius with its center at the origin, and the goal sets are the origin. The goal of the group of pursuers is the capture of at least one evader by a given number of pursuers. In terms of the initial positions and parameters of the game, a sufficient condition for capture is obtained. The method of resolving functions, which is used as a basis for analysis, provides sufficient conditions for solvability of the problem of pursuit in some guaranteed time.
differential games, pursuer, evader, capture, multiple capture, conflict-controlled processes
The Methods for Aviation Systems’ Safety Analysis during Combinations of Dangerous Heterogeneous Events Including Human Factor
This study presents a probabilistic method for assessing the safety and reliability of aviation systems based on modeling transitions between functional and failed elementary states. The analysis includes five core components of the aircraft system: crew, engines, avionics, power supply, and structural elements. Using failure and recovery flow intensities derived from realworld data for various aircraft types in 2022, the authors construct a system of differential equations to calculate dynamic safety indicators. The method applies state-transition graphs and formal mathematical models to describe the system’s behavior under different conditions. Particular attention is given to the non-technical elementary state representing crew condition, with a refined classification of critical human factor events such as specific headache types. The study performs calculations in MATLAB and provides comparative safety assessments for multiple aircraft models, such as Airbus (A-319 and A-320), Bombardier CRJ200, Boeing (737, 747 and 777), Sukhoi Superjet 100 (RRJ-95) and An-26B-100.
Optimization of Multi-Currency Deposit Structure by Two Indicators (Income and Risk) under Uncertainty
A two-criteria vector optimization problem – finding Pareto-optimal solutions in linear systems with interval uncertainty of coefficients – is considered. The problem of resource allocation to multiple activities is investigated. The uncertainty-adjusted income is a bilinear function, linear by strategy under fixed uncertainty and by uncertain parameters under fixed strategy. Guaranteed income is a linear function of variables and guaranteed risk is a piecewise linear function. Finding the optimal guaranteed risk is reduced to a linear programming problem by piecewise linear programming methods. To solve the two-criteria problem of the optimal allocation of financial resource on three currency deposits, the parameterization of the Pareto set by the value of the guaranteed income criterion is applied. Thus, the construction of a representative subset of Pareto-optimal solutions is reduced to solving a finite number of linear programming problems. The results can be used in analyzing the problems of financial management under conditions of incomplete information.
deposit diversification, bicriteria optimization, incomplete information, minimax regret solution
Grading Structure for Derivations of Group Algebras
In this paper we give a way of equipping the derivation algebra of a group algebra with the structure of a graded algebra. The derived group is used as the grading group. For the proof, the identification of the derivation with the characters of the adjoint action groupoid is used. These results also allow us to obtain the analogous structure of a graded algebra for outer derivations. A non-trivial graduation is obtained for all groups that are not perfect.
derivations, bimodule, outer derivations
Ensuring the Sustainability of Health Care Management Expert Support and Decision Making in Modern Conditions
Current technological and environmental changes requiring new approaches for healthcare data generation and assessment as well as decision-making support. The analysis performed using Delphi method indicated that sustainability of healthcare decision-making by using a number of approaches based on existing opportunities for proactive risk-based assessment of population health and healthcare interventions. Non-numerical qualitative expert opinions are of the same value as quantitive data while the balance between them and the methodology of mutual transformation form an integrated evidence-based support for the sustainable data generation and healthcare decision-making. Qualitative expert opinions make it also possible to decrease the asymmetry and lack of quantitative data between model studies on animals and the characteristics of the human body. The balance between qualitative expert assessment and the digital evidence changes during the lifecycle of the intervention or possibly process (like pandemic). Sustainability of healthcare decision-making in changing environment depends on availability and methods of qualitative expert support. Currently, there are no generally accepted methods for the final qualitative expert assessment, which makes it possible to reduce the diversity of interdisciplinary big data to a transparent and understandable assessment and these methodology and methods are to be developed. Automated systems for early detection of emergent cases based on medical statistics data are also of great importance and capable increasing sustainability of healthcare management and this information should be linked to pre-prepared action plans to avoid COVID-19 lessons in future.
sustainability, healthcare management, decision-making, expert support, public health emergencies, COVID-19 lessons, data generation, quantitative data, qualitative data, proactive, risk-based.
Stability Criteria for Periodic Selector-Linear Difference Inclusions
The paper considers periodic selector-linear difference inclusions. Lyapunov functions from a parametric class of homogeneous forms of even degree are constructed. These functions establish necessary and sufficient conditions of asymptotic stability and can be used in the development of numerical methods for investigating the stability of the systems equivalent to the considered difference inclusions. Using piecewise linear Lyapunov functions, an algebraic criterion of asymptotic stability of the considered inclusions is obtained. An example of a mechanical system leading to periodic selector-linear difference inclusion is considered.
algebraic criterion of asymptotic stability
A Cauchy Problem for Functional Inclusions with Causal Operators in Banach Spaces
In this paper, we consider the Cauchy problem for functional inclusions containing the sum of n causal single-valued operators and a multivalued causal operator in Banach spaces. The peculiarity of single-valued operators is that, starting from the second term, each operator is represented by an integral with a variable upper limit of the previous term. Such functional inclusions generalize the Cauchy problem for semilinear differential equations and inclusions of arbitrary order n, as well as a Cauchy-type problem in the case of inclusions and equations of fractional order not exceeding n. To solve the problem, we will apply the theory of topological degree for multivalued condensing mappings. To prove the existence of a solution, we will construct a resolving multivalued operator in the space of continuous functions corresponding to the problem. Based on the properties of the resolving operator, we will prove a theorem on the existence of solutions to this problem.
causal multioperator, functional inclusion, Cauchy type problem, differential inclusion, fractional derivative, measure of non-compactness, fixed point, topological degree, condensing multioperator
The Multivalued Solutions of the Cauchy Problem for One Quasilinear System
The article proposes a generalization of the method of characteristics to quasilinear systems of evolutionary equations with one spatial variable. Such systems are a special case of hydrodynamic type systems. It is shown that in some cases self-intersection of solution graphs is possible. An example of a system of two equations is considered in detail.
Hydrodynamic type systems, multivalued solutions, jet spaces, caustics, selfintersection, Cauchy problem
Does Political Instability Affect on Business Efficiency of Russian Firms?
This study delves into the impact of political instability on the business efficiency (proxied by growth rate of ROA) of 3,706 Russian firms for the period 2019-2022. The aim of the study is to reveal the impact of governance quality on the managerial efficiency of Russian companies during recent years with a particular concern of the on-going political instability: the Russia-Ukraine conflict. The results from the binary probit regression analysis allow us to substantiate that the probability of ROA growth and governance quality are inversely related in the recent years. However, when the governance indicators are interacted with the year dummy 2022, its effect becomes positive on the probability of growth of ROA. This implies that due to the ongoing Russia-Ukraine conflict the improved governance quality starts to exert impacts on the business efficiency of Russian firms. The overall impact of governance indicators is stronger for SMEs than for large companies in Russia, indicating that large companies have better capacity to withstand external shocks and instabilities than SMEs.
Copyright (c) 2024 Advances in Systems Science and Applications
Adaptive Disturbance Rejection Control of 2D Crane Based on DREM with Instrumental Variables
A problem of control of uncertain 2D overhead crane affected by disturbances with unknown model is considered. An adaptive controller is proposed to solve the above-mentioned problem, which main salient feature is that it ensures asymptotic convergence of errors for both trolley position and payload swing angle not to a bounded set, but to zero without requirement of it a priori knowledge on bounds of the system parameters and disturbance. First of all, the crane is represented in the feedback linearizable form via coordinate transformations under mild assumptions. Then such representation is parameterized in the form of perturbed linear regression equation, which parameters are exactly identified via application of procedure, which has been recently proposed by the authors and is based on the dynamic regressor extension and mixing method and instrumental variables approach. Obtained parameters estimates are substituted into derived ideal control law, and asymptotic stability of the proposed adaptive control system is rigorously proved. All theoretical results are validated via numerical experiments.
On the External Estimation of the Limit Reachable Set for the Linear Discrete-Time System Based on Support Hyperplanes
A linear discrete-time system with geometric constraints on control is considered. For the given system, the problem of constructing the limit reachable set is solved. It is proven that it is a cylinder oriented along certain elements of the real Jordan basis. Statements about the structure of the supporting hyperplane to the convex section of this cylinder are formulated and proven. Necessary and sufficient conditions for the boundedness of the limit reachable set are determined.
discrete-time system, limit reachable set, support hyperplane, convex set, polyhedral approximation
The Problem of Dynamic Regulation of Train Formation on a Marshalling Yard
The problem of dynamic freight trains formation at a railway station is considered. This problem is part of a two-step strategy to create a dynamic train formation plan. It is assumed that technical routes of all cars and the predicted arrival time of new groups of cars at the station are known. The problem is to determine the set of cars and the departure time of each train formed at this station, taking into account the availability of locomotives and restrictions on the length of trains. The goal is to minimise the total waiting time for cars at the station. Mathematical models for different versions of the problem are presented as an integer and a mixed integer linear programming problems. Results of computational experiments allow to estimate the influence of the amount of information about arriving trains to the station on the value of the objective function.
On the Compatibility of Metric and Linear Order
There is a classic question of introducing some reasonable order on the real plane R2. We consider this problem through the prism of the relation between metric proximity and linear order proximity, introducing a way to determine the compatibility relation between metric and linearly ordered spaces, and study the basic properties of this connection. For R and its metric subspaces, the order on the line is compatible with the metric according to the definition we introduce. It turns out that for Rn for n > 1, as well as for other similar metric spaces in which there is a subspace isometric to an open ball in Rn, it is impossible to introduce an order that is compatible with the metric. At the same time, we also introduce a family of spaces called discrete curved lines, which are not generally isometric to the subspaces of R, but for which it is possible to introduce a linear order compatible with the natural metric on them. For them we prove sufficient conditions for the compatibility of the metric with the order. Using them, we construct spaces with non-trivial properties in which the order is compatible with the metric. In particular, we show that although on all of Rn no order is compatible with the metric, in any normed space one can introduce non-trivial metric subspaces compatible with some order (in the case of infinite-dimensional normed spaces, this subspace can be constructed to be non-embeddable in any finite-dimensional subspace).
Estimating the Unmeasured Output of Nonlinear SISO System under Uncertainty
Nonlinear single-channel control plant with affine unmached external disturbances are considered. Their mathematical model has the so-called triangular (based on the composition of the arguments of the functions in each equation) “input-output” form, which has the following structural properties. If there are no external disturbances, then this form is controllable and observable in terms of output. If external disturbances are smooth, then the control plant model is representable in the canonical “input-output” form with respect to mixed variables (functions of state variables, external disturbances and their derivatives). In the new mixed variable basis, the system remains controllable, observable, and has the same relative degree as the original system. If the output variable is measured, then an observer of mixed variables can be constructed based on the canonical system and, using suitable feedback, ensure the desired behavior of the output variable. In this case, there is no need to detail external disturbances and design individual observers for them, which greatly simplifies the structure of the controller. This paper discusses the problem of implementing the specified synthesis procedure in the case when the output variable is not measured. Motivating examples are given and conditions are formulated under which it is possible to first restore the output variable from the measurement of other state variables invariantly with respect to the action of external disturbances. Methods for estimating external disturbances using observers with piecewise linear corrective actions, which do not require the introduction of dynamic disturbance models, constitute the methodological basis for solving this problem. Using the example of various mathematical models of single-link manipulators, the fulfillment/failure of the conditions necessary to restore an unmeasured output variable is demonstrated. The proposed approach can be extended to multichannel nonlinear control plants without loss of generality.
nonlinear SISO system, unmatched disturbances, observability, reduced-order state observer, piecewise linear function with saturatio single-link manipulator.
Emerging Perspectives on Multiband Fractaland Hybrid Fractal Antennas for Wireless Applications: A Comprehensive Analysis
In the rapidly evolving field of wireless communications, the demand for compact, efficient, and versatile antenna systems has led to significant interest in multiband hybrid fractal antennas. This paper presents a brief overview to the basic fractal structures and their utilization to develop hybrid fractal patch antenna design. The key interest areas are multiband behaviour, acceptable return loss, voltage standing wave ratio, gain and reduced complexity. Many studies have simulated and examined the antenna using the Finite-Difference Time-Domain (FDTD) and Finite Element Method (FEM) based techniques. Various antenna performance parameters such return loss, resonant frequency, bandwidth, and gain are observed and the findings of several articles have been presented. The compact size, multiband/wideband features, and extensive utility in wireless applications make the fractal antenna a promising field of study. These antennas are so popular because of their electrically vast construction, which neatly folds into small spaces.
Microstrip Patch Antenna, Fractal structure, Hybrid Fractals, Multiband, Return loss, Iterated function system (IFS)
Analysis of Ring Laser Gyroscope Cavity Thermal deformations
Ring laser gyroscopes are crucial for high-precision orientation, stabilization, and autonomous inertial navigation systems. However, their operational accuracy is significantly affected by temperature-induced cavity deformations, leading to potential performance degradation and data loss. This study addresses this challenge by developing a robust algorithm in the MATLAB environment designed to simulate the temperature deformations of a ring laser cavity. Leveraging experimental data, the methodology enables the precise modeling of cavity deformation behavior at various stages of the ring laser gyroscope assembly. The developed mathematical model effectively demonstrates how the addition of structural elements influences the cavity's thermal response and overall deformation. This research provides a novel approach to quantitatively estimate the contribution of individual structural components to the total thermal deformation. The findings offer critical insights for optimizing ring laser gyroscope design, thereby enhancing their accuracy, reliability, and resilience in diverse operational conditions.
Enhancing Comfort and Stability of a Vehicle Suspension System when Oscillating by an Optimal Hybrid Control Algorithm
This article proposes a control algorithm for an automotive suspension system to improve ride comfort. The control method is based on the combination of Sliding Mode Control (SMC) and Proportional-Integral-Derivative (PID), with parameters optimally selected by an inloop algorithm called OSMCPID. The system's performance is evaluated by simulation, which goes through three specific cases. According to the article's findings, in the first two cases, the average value of vehicle body displacement when using the proposed algorithm is only 7.71% and 6.96%, respectively, compared to mechanical suspension. In the third case, vehicle body displacement approaches zero once the road excitation signal ends. Meanwhile, the remaining cases have a more significant gap. In addition, the phase difference of the control signal is slight, while the chattering phenomenon almost does not occur when using the hybrid algorithm. In general, the system can adapt to changing external conditions.
Application of Modular Neural Networks for Image Recognition in Foggy Computing Environments
The paper considers various approaches to the decomposition of artificial neural networks for the purpose of their application on fog computing nodes. Based on the requirements for the organization of fog computing, a method of dividing the input information into subspaces by means of wavelet transform and subsequent proportional division of all layers of the neural network is proposed. The proposed approach achieves a significant gain in the amount of information transferred between modules compared to the currently used layer-by-layer partitioning. In addition, the proposed method optimizes the load on fog computing nodes by partially utilizing the modules.
proportional division of layers of the neural network
Possibilities of Assessing Information Security RisksUsing Fuzzy Logic and Econometrics Methods
The paper provides an overview of publications devoted to the assessment methods of information security risks in various systems, including those with network structures and using cloud technologies. In most studies, risk assessment and management include the construction of models that adequately show the occurrence of adverse conditions, taking into account various parameters that affect risk. These methods help to make decisions in order to reduce the potential damage that can be caused by external attacks on information resources or by realization of other threats through existing vulnerabilities. However, they provide an acceptable result in risk assessment in conditions where it is possible to quantify the parameters on which the risk depends. In conditions of high uncertainty, for example, when determining the dependence of risk on subjective factors, the use of these methods can lead to high errors. The authors propose the method of the combined use of fuzzy logic and regression analysis, which allows us to solve the problem of assessing the risk of information security in conditions of the uncertainty dependence of various parameters in complex information structures. It also allows you to set parameters on which the information security risk depends in a greater extent, and a list of parameters that you can ignore in the assessed situation. Using this method, you can plan measures to improve protection of the information system in both the short and long term.
information security, information leakage, multifactorial risk assessment, fuzzy logic, econometrics, production rules, regression equation, multiple determination coefficient, subjective factors, uncertainty conditions.
The Introduction of Cloud Storage as One of the Ways to Save the Organization's Data Management Resource
The article discusses the use of cloud technologies in enterprise data management, provides examples of the use of cloud technologies. The analysis of the problems of implementation and functioning of cloud data storages in organizations has been carried out. Based on the analysis, the technological and functional problems of implementing cloud data storages are highlighted. The attention is focused on unsolvable problems of building distributed data transmission systems. The practical implementation of cloud storage and data exchange processes through it has been carried out. A comparative analysis of the proposed methods with existing ones is demonstrated and their effectiveness is proved.
Study of Three Dimensional Casson-Nanofluid Flow due to a Linear Porous Stretching Sheet in the Presence of Double Diffusion Effects
The object of this research is to examine the combined effects of mass and thermal Biot numbers on the properties of a Powell-Erying fluid flow that is two-dimensional, constant, viscous, incompressible, and non-Newtonian. In the direction of the flow is an extending sheet encircled by a porous medium. Further consideration is given to the existence of a chemical reaction, thermophoresis, Brownian motion, and velocity lapse, among other factors. Utilizing the Powell-Erying Cauchy non-Newtonian model, the viscoelastic effect is accounted for. When establishing concentration and temperature boundary conditions, thermal and mass Biot numbers are incorporated. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge-Kutta method. By utilizing graphs, one can examine the impacts of a variety of engineering parameters on concentration profiles, velocity, and temperature. This is accomplished through the implementation of numerical solutions derived via the Runge-Kutta method. Furthermore, the Nusselt number, Skin-friction, and Sherwood number coefficients are evaluated and shown in a tabular format utilizing the same parameters. In the end, the numerical outcomes obtained from this investigation are substantiated and considered to be highly consistent with the findings that were previously documented.
Green Industry: Energy Efficiency Improvement of Steam Generation in a Moroccan Plastic Recycling Industry
Steam systems in industry represent a substantial share of industrial energy consumption. Therefore, improving the energy efficiency of these systems is necessary to reduce fossil fuel consumption and greenhouse gas emissions in the context of energy transition. This improvement not only leads to environmental benefits but also enhances financial gains, thereby increasing industrial competitiveness. The objective of this study is to identify energy-saving opportunities in a plastic recycling plant in Morocco while adopting a system approach based on thermodynamics fundamentals. After conducting a benchmark analysis based on a scoping tool questionnaire, the steam generation section is diagnosed to quantify major losses. Subsequently, an action plan is suggested for more efficient thermal energy use. The assessments focus on energy loss reductions along with waste heat recovery. The implementation of these actions results in a potential saving of 22%, achieving an energy gain of 5574 GJ/y, a financial benefit of 96 884 $/y, and a reduction in CO2 emissions by 332.15 tons annually. The global payback period does not exceed one year. The study conducted encourages the adoption of cost-effective energy efficiency measures by industry stakeholders, in line with the Sustainable Development Goals. Furthermore, it benefits all industries utilizing boilers in their steam production systems, regardless of the diversity of industrial systems.
steam systems, industrial energy consumption, energy efficiency, greenhouse gas emissions, energy-saving opportunities, waste heat recovery, energy transition, sustainable development
The Approximation Matrix Method and its Comparison with the Analytical Hierarchy Process by T. Saaty
The article presents an optimization method for the formation of quantitative weights of objects (importance of criteria, priorities of alternatives) according to the initial expert judgment matrix in multi-criteria selection problems. Since the matrix of pairwise comparisons can be considered as some perturbation of the multiplicative matrix, the proposed method is based on the approximation of the original matrix of pairwise comparisons by the multiplicative matrix according to the matrix criterion of minimum distances between matrices. There is a one-to-one mapping between the elements of the weight vectors and the elements of the multiplicative matrix. For the first time, using a specific example using the matrix criterion, a relative estimate of the approximate solution of the Analytical Hierarchy Process by T. Saaty concerning the optimal solution obtained by the approximation matrix method is given. On account of the approximation matrix method being mathematically justified and due to the simplicity of finding optimal solutions, it can be recommended instead of the Analytical Hierarchy Process by T. Saaty.
The Mean-Field Approximation for the SCARDO Model in the Case of 3-element Opinion Space: Fixed Points and Exact Solutions
We analyze the SCARDO model in the case of the 3-element opinion space under specific constraints on the transition table parameters that allows to link the problem at stake to the case of the 2-element opinion space that has been thoroughly studied previously. We characterize the properties of fixed points and support our findings by numerical experiments. Further, we manage to find out those settings that ensure the system almost surely reaches a specific domain in the phase space, after which its behavior can be predicted analytically.
Practical Applicability of the Metric Approach for a Scheduling Problem
A given special case of NP-complete scheduling problem can be approximated by solving a special case of similar problem with the same precedence graph. We construct a metric space over a set of special cases of this problem and consider the statistical relationship between distance between a pair of special cases of the under consideration and the average error of the approximated solution. Sethi, Gabow, Coffman's and Fujii's algorithms for this problem are used. It is shown that the absolute and the relative error of the objective function decreases over the density of a graph with a fixed number of jobs. In general case, relative non-zero error value increases with the number of jobs.
Exploring the Relationship between Cardiac Disease and Patterns of 12-Lead ECG through Neural Network: A Comprehensive Review
Heart disease is a significant public health concern, affecting a large number of people worldwide daily. With a shortage of qualified cardiologists, particularly in low-income countries, the diagnosis and management of heart disease can be challenging. The electrocardiogram (ECG) is the primary diagnostic tool for heart disease, but interpreting ECG reports requires the expertise of a qualified cardiologist, making it time-consuming and costly. To address this issue, automated ECG signal interpretation is necessary. Hence, this article has made an encyclopedic review of the existing literature. The article includes demonstration of frequently utilized data sets and tools and techniques for this domain. Therefore, a framework is proposed based on the observation of existing works. The proposed framework aims to improve the analysis of ECG reports for both cardiologists and non-experts. Our framework considers the 12-lead ECG, the different types of leads, wave patterns, and their relationship with heart disease. The objective is to produce reliable and accurate results while reducing analysis time. The proposed framework is inherent to improve the diagnosis and management of heart disease by enabling a wider range of healthcare providers and individuals to interpret ECG reports. This could lead to earlier detection and treatment of heart disease, which could improve outcomes and save lives.
Correlations of the Sojourn Times of Subtasks in Fork-Join Queueing Systems with M|M|1-type Subsystems
The article analyzes the relationship between the residence times of subtasks in the fork-join subsystems of the queuing system. When arriving the fork-join system, the task is divided into subtasks, each of which is serviced in its own subsystem, the task is considered serviced after the completion of all subtasks that originally comprised it servicing. There is a dependence between the residence times of subtasks in subsystems, which affects the main performance indicators of the system, for example, the response times, which greatly complicates their analysis. The paper examines the characteristics of the existing dependence. In particular, with the help of generating functions and the Laplace-Stieltjes transformation, exact expressions for the Pearson and Spearman correlation coefficients are obtained. In addition, using a combination of several methods, including the Nelder-Mead optimization method, the estimation of the Kendall correlation coefficient was obtained, and the model for the response time estimation based on the resulting correlation coefficients was described. Despite the many works on the study of fork-join queuing systems, there are practically no articles devoted to the correlation analysis of the temporal metrics of the model. Therefore, this article can become one of the first in this area, laying the foundation for the study of the correlation dependence and its influence on the performance parameters of the model, not only for the classical case of M|M|1 subsystems, but also for more complex architectures of this system.