Search Results (42)

This paper addresses the problem of decision-making support for the modernization of distributed automated control systems (ACS) in power engineering by proposing an integral quality criterion that combines similarity-driven Markov process modeling with geometric programming. The methodology transforms the transition rate matrix of a continuous-time Markov chain (CTMC) into a matrix polynomial, enabling the derivation of normalized similarity indices and the development of a criterion-based model to quantify relative variations in system quality without requiring global optimization. The proposed approach yields a generalized criterion model that facilitates the ranking of modernization alternatives and the evaluation of the sensitivity of optimal decisions to parameter variations. The practical implementation is demonstrated through updated state transition graphs, quality functions, and UML-based architectures of diagnostic-ready evaluation modules. The scientific contribution of this work lies in the integration of similarity-based Markov modeling with the mathematical framework of geometric programming into a unified criterion model for the quantitative assessment of functional readiness under multistate conditions and probabilistic failures. The methodology enables the comparison of modernization scenarios using a unified integral indicator, assessment of sensitivity to structural and parametric changes, and seamless integration of quality evaluation into SCADA/Smart Grid environments as part of real-time diagnostics. The accuracy of the assessment depends on the adequacy of transition rate identification and the validity of the Markovian assumption. Future extensions include the real-time estimation of transition rates from event streams, generalization to semi-Markov processes, and multicriteria optimization considering cost, risk, and readiness. Full article

The article presents a methodology for assessing the mission state of the MBG-AUV, designed to support the decision to continue or abort a task in a traceable manner. The approach combines a five-state operational graph (S0–S4) with telemetry through a Markov chain, whose transition intensities are determined directly from onboard and environmental signals. The data are synchronized in UTC time, subject to quality control and unit standardization, and subsequently transformed into cumulative exposure (hazard) and risk as a function of time. For the analyzed 60 min coastal mission profile, the end-of-mission risks were R_Comm(T) ≈ 0.29, R_Hull(T) ≈ 0.011 and R_Power(T) ≈ 0.006, with the first warning threshold (αₑ = 0.10) crossed after approximately 20 min at a depth of ~167 m. These values quantify the dominant contribution of acoustic communication to the overall mission risk. At the mission level, we report two complementary assessments—a weighted average (with operationally defined subsystem weights) and an assessment under the assumption of independence, along with the time of first warning, subsystem contribution ranking, and “hot” segments of the profile. The difference between the weighted mission estimate and the independence-based estimate was approximately 0.03 by the end of the mission, indicating the operational relevance of weight selection. A case study indicates that coastal missions are typically dominated by acoustic link limitations while maintaining comfortable energy and structural margins. The methodology preserves notational consistency, is straightforward to implement in ground or onboard tools, and is scalable to the full set of seven subsystems and subsequent profiles. The future work includes modeling parameter uncertainties, inter-subsystem couplings, and platform loss, as well as integration with trajectory planning to limit exposure. Full article

Cyber defense has evolved into an algorithmically intensive discipline where mathematical rigor and adaptive computation underpin the robustness and continuity of digital infrastructures. This review consolidates the algorithmic spectrum that supports modern cyber defense, from cryptographic primitives that ensure confidentiality and integrity to behavioral intelligence algorithms that provide predictive security. Classical symmetric and asymmetric schemes such as AES, ChaCha20, RSA, and ECC define the computational backbone of confidentiality and authentication in current systems. Intrusion and anomaly detection mechanisms range from deterministic pattern matchers exemplified by Aho-Corasick and Boyer-Moore to probabilistic inference models such as Markov Chains and HMMs, as well as deep architectures such as CNNs, RNNs, and Autoencoders. Malware forensics combines graph theory, entropy metrics, and symbolic reasoning into a unified diagnostic framework, while network defense employs graph-theoretic algorithms for routing, flow control, and intrusion propagation. Behavioral paradigms such as reinforcement learning, evolutionary computation, and swarm intelligence transform cyber defense from reactive automation to adaptive cognition. Hybrid architectures now merge deterministic computation with distributed learning and explainable inference to create systems that act, reason, and adapt. This review identifies and contextualizes over 50 foundational algorithms, ranging from AES and RSA to LSTMs, graph-based models, and post-quantum cryptography, and redefines them not as passive utilities, but as the cognitive genome of cyber defense: entities that shape, sustain, and evolve resilience within adversarial environments. Full article

Stealth attacks targeting industrial control systems (ICS) exploit subtle sequences of malicious actions, making them difficult to detect with conventional methods. The OPC Unified Architecture (OPC UA) protocol—now widely adopted in SCADA/ICS environments—enhances OT–IT integration but simultaneously increases the exposure of critical infrastructures to sophisticated cyberattacks. Traditional detection approaches, which rely on instantaneous traffic features and static models, neglect the sequential dimension that is essential for uncovering such gradual intrusions. To address this limitation, we propose a hybrid sequential anomaly detection pipeline that combines Markov chain modeling to capture temporal dependencies with machine learning algorithms for anomaly detection. The pipeline is further augmented by explainability through SHapley Additive exPlanations (SHAP) and causal inference using the PC algorithm. Experimental evaluation on an OPC UA dataset simulating Man-In-The-Middle (MITM) and denial-of-service (DoS) attacks demonstrates that incorporating a second-order sequential memory significantly improves detection: F1-score increases by +2.27%, precision by +2.33%, and recall by +3.02%. SHAP analysis identifies the most influential features and transitions, while the causal graph highlights deviations from the system’s normal structure under attack, thereby providing interpretable insights into the root causes of anomalies. Full article

New copula families are constructed based on orthogonality in $L^2(0,1)$. Subclasses of idempotent copulas with square integrable densities are derived. It is shown that these copulas generate exchangeable Markov chains that behave as independent and identically distributed random variables conditionally on the initial variable. We prove that the extracted family of copulas is the only set of symmetric idempotent copulas with square integrable densities. We extend these copula families to asymmetric copulas with square integrable densities having special dependence properties. One of our extensions includes the Farlie–Gumbel–Morgenstern (FGM) copula family. The mixing properties of Markov chains generated by these copulas are established. The Spearman’s correlation coefficient ${\rho }_S$ is provided for each of these copula families. Some graphs are also provided to illustrate the properties of the copula densities. Full article

Even though Kemeny’s constant was first discovered in Markov chains and expressed by Kemeny in terms of mean first passage times on a graph, it can also be expressed using the pseudo-inverse of the Laplacian matrix representing the graph, which facilitates the calculation of a sharp upper bound of Kemeny’s constant. We show that for certain classes of graphs, a previously found bound is tight, which generalises previous results for bipartite and (generalised) windmill graphs. Moreover, we show numerically that for real-world networks, this bound can be used to find good numerical approximations for Kemeny’s constant. For certain graphs consisting of up to 100 K nodes, we find a speedup of a factor 30, depending on the accuracy of the approximation that can be achieved. For networks consisting of over 500 K nodes, the approximation can be used to estimate values for the Kemeny constant, where exact calculation is no longer feasible within reasonable computation time. Full article

The sheaf cohomology techniques are newly used to include Morse simplicial complexes in a rectangular-matrix chain, whose singular values are compatible with those of a square matrix, which can be used for multiple sequencing. The equivalence with the simplices of the corresponding graph is proven, as well as that the filtration of the corresponding probability space. The new protocol eliminates the problem of stochastic stability of deep Markov models. The paradigm can be implemented to develop deep-machine-learning multiple sequencing. The construction of the deep Markov models for sequencing, starting from a profile Markov model, is analytically written. Applications can be found as an amino-acid sequencing model. As a result, the nucleotide-dependence of the positions on the alignments are fully modelized. The metrics of the manifolds are discussed. The instance of the application of the new paradigm to the Jukes–Cantor model is successfully controlled on nucleotide-substitution models. Full article

Background/Objective: Environmental exposures, such as heavy metals, can significantly affect physical activity, an important determinant of health. This study explores the effect of physical activity on combined exposure to cadmium, lead, and mercury (metals), using data from the 2013–2014 National Health and Nutrition Examination Survey (NHANES). Methods: Physical activity was measured with ActiGraph GT3X+ devices worn continuously for 7 days, while blood samples were analyzed for metal content using inductively coupled plasma mass spectrometry. Descriptive statistics and multivariable linear regression were used to assess the impact of multi-metal exposure on physical activity. Additionally, Bayesian Kernel Machine Regression (BKMR) was applied to explore nonlinear and interactive effects of metal exposures on physical activity. Using a Gaussian process with a radial basis function kernel, BKMR estimates posterior distributions via Markov Chain Monte Carlo (MCMC) sampling, allowing for robust evaluation of individual and combined exposure-response relationships. Posterior Inclusion Probabilities (PIPs) were calculated to quantify the relative importance of each metal. Results: The linear regression analysis revealed positive associations between cadmium and lead exposure and physical activity. BKMR analysis, particularly the PIP, identified lead as the most influential metal in predicting physical activity, followed by cadmium and mercury. These PIP values provide a probabilistic measure of each metal’s importance, offering deeper insights into their relative contributions to the overall exposure effect. The study also uncovered complex relationships between metal exposures and physical activity. In univariate BKMR exposure-response analysis, lead and cadmium generally showed positive associations with physical activity, while mercury exhibited a slightly negative relationship. Bivariate exposure-response analysis further illustrated how the impact of one metal could be influenced by the presence and levels of another, confirming the trends observed in univariate analyses while also demonstrating the complexity varying doses of two metals can have on either increased or decreased physical activity. Additionally, the overall exposure effect analysis across different quantiles revealed that higher levels of combined metal exposures were associated with increased physical activity, though there was greater uncertainty at higher exposure levels as the 95% credible intervals were wider. Conclusions: Overall, this study fills a critical gap by investigating the interactive and combined effects of multiple metals on physical activity. The findings underscore the necessity of using advanced methods such as BKMR to capture the complex dynamics of environmental exposures and their impact on human behavior and health outcomes. Full article

We consider the problem of finding the largest clique of a graph. This is an NP-hard problem and no exact algorithm to solve it exactly in polynomial time is known to exist. Several heuristic approaches have been proposed to find approximate solutions. Markov Chain Monte Carlo is one of these. In the context of Markov Chain Monte Carlo, we present a class of “parallel dynamics”, known as Probabilistic Cellular Automata, which can be used in place of the more standard choice of sequential “single spin flip” to sample from a probability distribution concentrated on the largest cliques of the graph. We perform a numerical comparison between the two classes of chains both in terms of the quality of the solution and in terms of computational time. We show that the parallel dynamics are considerably faster than the sequential ones while providing solutions of comparable quality. Full article

Network functions virtualization (NFV) has become the platform for decomposing the sequence of virtual network functions (VNFs), which can be grouped as a forwarding graph of service function chaining (SFC) to serve multi-service slice requirements. NFV-enabled SFC consists of several challenges in reaching the reliability and efficiency of key performance indicators (KPIs) in management and orchestration (MANO) decision-making control. The problem of SFC fault tolerance is one of the most critical challenges for provisioning service requests, and it needs resource availability. In this article, we proposed graph neural network (GNN)-based deep reinforcement learning (DRL) to enhance SFC fault tolerance (GRL-SFT), which targets the chain graph representation, long-term approximation, and self-organizing service orchestration for future massive Internet of Everything applications. We formulate the problem as the Markov decision process (MDP). DRL seeks to maximize the cumulative rewards by maximizing the service request acceptance ratios and minimizing the average completion delays. The proposed model solves the VNF management problem in a short time and configures the node allocation reliably for real-time restoration. Our simulation result demonstrates the effectiveness of the proposed scheme and indicates better performance in terms of total rewards, delays, acceptances, failures, and restoration ratios in different network topologies compared to reference schemes. Full article

Clustered data are a complex and frequently used type of data. Traditional factor analysis methods are effective for non-clustered data, but they do not adequately capture correlations between multiple observed individuals or variables in clustered data. This paper proposes a Bayesian approach utilizing MCMC and Gibbs sampling algorithms to accurately estimate parameters of interest within the clustered factor analysis model. The mean traversal graph of parameters ensures that the Markov chain converges, and the Bayesian case-deletion model is used to analyze the model’s impact and identify outliers in clustered data using Cook’s posterior mean distance. The applicability and validity of the principal-component-method-based factor analysis model for clustered data are demonstrated by comparing the parameter estimation of this method with the principal component method, the clustered data with and without internal relationships are compared by example analysis, and the anomalous groups are identified by the Cook’s posterior mean distance. Full article

The article presents the results of a study on modeling cloud systems. In this research, the authors developed both analytical and simulation models. System analysis was conducted at the level of virtual machine support, corresponding to Infrastructure as a Service (IaaS). The models assumed that virtual machines of different sizes are offered as part of IaaS, reflecting the heterogeneous nature of modern systems. Additionally, it was assumed that due to limitations in access to physical server resources, only a portion of these resources could be used to create virtual machines. The model is based on Markov chain analysis for state-dependent systems. The system was divided into an external structure, represented by a collection of physical machines, and an internal structure, represented by a single physical machine. The authors developed a novel approach to determine the equivalent traffic, approximating the real traffic appearing at the input of a single physical machine under the assumptions of request distribution. As a result, it was possible to determine the actual request loss probability in the entire system. The results obtained from both models (simulation and analytical) were summarized in common graphs. The studies were related to the actual parameters of commercially offered physical and virtual machines. The conducted research confirmed the high accuracy of the analytical model and its independence from the number of different instances of virtual machines and the number of physical machines. Thus, the model can be used to dimension cloud systems. Full article

Predicting vehicle mobility is crucial in domains such as ride-hailing, where the balance between offer and demand is paramount. Since city road networks can be easily represented as graphs, recent works have exploited graph neural networks (GNNs) to produce more accurate predictions on real traffic data. However, a better understanding of the characteristics and limitations of this approach is needed. In this work, we compare several GNN aggregated mobility prediction schemes to a selection of other approaches in a very restricted and controlled simulation scenario. The city graph employed represents roads as directed edges and road intersections as nodes. Individual vehicle mobility is modeled as transitions between nodes in the graph. A time series of aggregated mobility is computed by counting vehicles in each node at any given time. Three main approaches are employed to construct the aggregated mobility predictors. First, the behavior of the moving individuals is assumed to follow a Markov chain (MC) model whose transition matrix is inferred via a least squares estimation procedure; the recurrent application of this MC provides the aggregated mobility prediction values. Second, a multilayer perceptron (MLP) is trained so that—given the node occupation at a given time—it can recursively provide predictions for the next values of the time series. Third, we train a GNN (according to the city graph) with the time series data via a supervised learning formulation that computes—through an embedding construction for each node in the graph—the aggregated mobility predictions. Some mobility patterns are simulated in the city to generate different time series for testing purposes. The proposed schemes are comparatively assessed compared to different baseline prediction procedures. The comparison illustrates several limitations of the GNN approaches in the selected scenario and uncovers future lines of investigation. Full article

Causal structure learning is one of the major fields in causal inference. Only the Markov equivalence class (MEC) can be learned from observational data; to fully orient unoriented edges, experimental data need to be introduced from external intervention experiments to improve the identifiability of causal graphs. Finding suitable intervention targets is key to intervention experiments. We propose a causal structure active learning strategy based on graph structures. In the context of randomized experiments, the central nodes of the directed acyclic graph (DAG) are considered as the alternative intervention targets. In each stage of the experiment, we decompose the chain graph by removing the existing directed edges; then, each connected component is oriented separately through intervention experiments. Finally, all connected components are merged to obtain a complete causal graph. We compare our algorithm with previous work in terms of the number of intervention variables, convergence rate and model accuracy. The experimental results show that the performance of the proposed method in restoring the causal structure is comparable to that of previous works. The strategy of finding the optimal intervention target is simplified, which improves the speed of the algorithm while maintaining the accuracy. Full article

Convolutional neural networks (CNNs) have been used widely to predict biological brain age based on brain magnetic resonance (MR) images. However, CNNs focus mainly on spatially local features and their aggregates and barely on the connective information between distant regions. To overcome this issue, we propose a novel multi-hop graph attention (MGA) module that exploits both the local and global connections of image features when combined with CNNs. After insertion between convolutional layers, MGA first converts the convolution-derived feature map into graph-structured data by using patch embedding and embedding-distance-based scoring. Multi-hop connections between the graph nodes are modeled by using the Markov chain process. After performing multi-hop graph attention, MGA re-converts the graph into an updated feature map and transfers it to the next convolutional layer. We combined the MGA module with sSE (spatial squeeze and excitation)-ResNet18 for our final prediction model (MGA-sSE-ResNet18) and performed various hyperparameter evaluations to identify the optimal parameter combinations. With 2788 three-dimensional T1-weighted MR images of healthy subjects, we verified the effectiveness of MGA-sSE-ResNet18 with comparisons to four established, general-purpose CNNs and two representative brain age prediction models. The proposed model yielded an optimal performance with a mean absolute error of 2.822 years and Pearson’s correlation coefficient (PCC) of 0.968, demonstrating the potential of the MGA module to improve the accuracy of brain age prediction. Full article