ABSTRACT. In the loss definition of Robust Variational Physics-Informed Neural Networks (RVPINNs) \cite{ROJAS2024116904}, accurately representing the variational residual is essential for ensuring stable and efficient training. Traditional numerical integration methods, such as fixed quadrature rules, may fail to adapt dynamically to the complexities of the solution, leading to suboptimal performance. Consequently, selecting integration points plays a crucial role in this process. In particular, choosing an insufficient number of points results in poor residual approximations, causing prematurely stagnant convergence. Conversely, using an excessive number of points increases the computational cost without necessarily improving the residual estimation as expected, thereby reducing the efficiency of the training process.

To address this challenge, we propose an Adaptive Integration Point Selection (AIPS) strategy that dynamically refines both the number and placement of integration points based on residual error estimations \cite{trynda5173427physics}. Rather than relying on a uniform or predetermined distribution, AIPS continuously adjusts the integration points throughout the training process, increasing their density in regions with high error while reducing them in well-approximated areas. This adaptive approach ensures that computational resources are allocated where they are most needed, enhancing both the accuracy of numerical integration and the efficiency of training.

Our method seamlessly integrates into the RVPINNs framework, preserving the advantages of variational formulations while overcoming the inefficiencies of fixed integration schemes. The refinement process is guided by an error-based criterion, ensuring that the weak-form residual is captured with high precision without incurring unnecessary computational overhead. By effectively balancing accuracy and efficiency, AIPS improves the stability and convergence rate of RVPINNs, making them more practical for solving complex partial differential equations. Furthermore, this strategy is highly flexible and can be extended to a wide range of problems that employ variational formulations and neural network-based solvers.

References

1. S. Rojas, P. Maczuga, J. Muñoz-Matute, D. Pardo, M. Paszyński, Robust variational physics-informed neural networks, Computer Methods in Applied Mechanics and Engineering 425 (2024) 116904. doi:https://doi.org/10.1016/j.cma.2024.116904. URL https://www.sciencedirect.com/science/article/pii/S0045782524001609

2. J. Trynda, P. M. Maczuga, A. Oliver, L. E. Garcia Castillo, R. F. Schaefer, M. Wozniak, Physics-informed neural network with adaptive mesh refinement, Available at SSRN 5173427.

ABSTRACT. This research explores the impact of structural limiting perception on the performance of Particle Swarm Optimization by restricting the range of information sharing among particles. By introducing localized communication models through Ring and Tree topologies, the study demonstrates significant improvements over the standard global-best PSO, particularly on a range of Traveling Salesman Problem instances from the TSPLIB. The results show that constraining particle perception enhances both solution quality and convergence behavior, with the Tree topology emerging as the most effective structure. The topological modifications maintain swarm diversity, prevent premature convergence, and facilitate continuous exploration while exploiting promising search regions. These findings suggest that structural constraints on information sharing can enhance PSO's robustness and effectiveness without adding computational complexity, offering a flexible approach applicable to various PSO variants and problem domains beyond TSP.

ABSTRACT. This paper introduces the Trust-Based Optimization (TBO), a novel extension of the island model in evolutionary computation that replaces conventional periodic migrations with a flexible, agent-based communication mechanism based on trust or reputation. Experimental results demonstrate that TBO generally outperforms standard island model evolutionary algorithms across various optimization problems. Nevertheless, algorithm performance varies depending on the problem type, with certain configurations being more effective for specific landscapes or dimensions. The findings suggest that trust and reputation mechanisms provide a flexible and adaptive approach to evolutionary optimization, improving solution quality in many cases.

ABSTRACT. Metaheuristics are excellent tools for solving difficult optimization problems. One of them is an island, easy-to-parallel model of evolutionary algorithm. We run them on High Performance Computing infrastructure, so it is important that they are well parallelized. So far, we have used standard topologies for migration, such as ring and torus. We want to check how it works in combination with promising random topologies, e.g. Erdos Renyi.

ABSTRACT. The goal of this paper is twofold. First, it explores hybrid evolutionary-swarm metaheuristics that combine the features of PSO and GA in a sequential, parallel and consecutive manner in comparison with their standard basic form: Genetic Algorithm and Particle Swarm Optimization. The algorithms were tested on a set of benchmark functions, including Ackley, Griewank, Levy, Michalewicz, Rastrigin, Schwefel, and Shifted Rotated Weierstrass, across multiple dimensions. The experimental results demonstrate that the hybrid approaches achieve superior convergence and consistency, especially in higher-dimensional search spaces. The second goal of this paper is to introduce a novel consecutive hybrid PSO-GA evolutionary algorithm that ensures continuity between PSO and GA steps through explicit information transfer mechanisms.

ABSTRACT. Knowledge of the human nanoscale connectome is critical for understanding how the brain works in health and disease. However, suitable data are yet unavailable and the numbers of circuits forming the connectome and neurons in each circuit are unknown. This work introduces nanoscale morphology connectomic wireframe and geometric models, each with 3 sub-models (straight and enhanced with parabolic and cubic branches); provides formulas for data bigness estimation for them; and estimates required storage. The connectome size/storage estimation is derived from that of the synaptome (all synapse set) assessed earlier. To accommodate for the great neuronal and synaptic variability, two cases of the number of brain neurons (86 and 100 billion) and three cases of the number of synapses/neuron (1,000;10,000; and 30,000) are considered with six connectomic models resulting in 36 storage estimation cases. The straight wireframe model requires from 8.51PB for 86 billion neurons and 1,000 synapses/neuron to 297PB for 100 billion neurons and 30,000 synapses/neuron. The straight geometric model needs from 10.58PB for 86 billion neurons and 1,000 synapses/neuron to 369PB for 100 billion neurons and 30,000 synapses/neuron. Model enhancement increases storage from 22.27PB for the parabolic wireframe model with 86 billion neurons and 1,000 synapses/neuron to 1,569PB for the cubic geometric model with 100 billion neurons and 30,000 synapses/neuron. The storage required for the human complete nanoscale connectome estimated for six models and 36 cases surpasses those available in today’s world's best supercomputers. This is the first work providing the bigness data estima-tion for the human nanoscale connectome.

ABSTRACT. Accurate prediction of enzyme thermostability is crucial for bioengineering applications. This paper proposes a novel ensemble learning framework for predicting protein thermostability. The proposed ensemble learning framework combines XGBoost, a potent gradient boosting technique, with a Bidirectional Long Short-Term Memory (BiLSTM) network, which captures complex sequence-based features. The proposed framework attained the RMSE, MAE, R2 score, and Spearman Correlation coefficient of 0.37, 0.68, 0.72, and 0.76 respectively. Its performance is also evaluated against other machine learning models and performs noticeably better than all of them. Furthermore, we leveraged Explainable Machine Learning (XML) techniques like SHAP (SHapley Additive Values), LIME (Local Interpretable Model Explainer), ELI5 and QLattice to enhance model interpretability.

ABSTRACT. Targeted drugs are widely used and developed as they reduce side effects for cancer patients. However, the turbulent blood flow may reduce their precision from their target, causing negative effects on other tissues. This research aims to overcome such limitations by developing a bio-robot with a turtle-like shape, which maintains stability in turbulent flow and moves in a direction responsive to the acidity of cancer cells. The robot is designed to effectively move towards cancer cells relying on two types of muscles: 1) a self-activated muscle that maintains the robot's stability in turbulent flow, mimicking the movement of sea turtle fins, and is controlled by muscle cells with different activation phases. The optimal coefficient of calcium diffusion for their activation is found at approximately 0.01 µm²/s; and 2) a pH-responsive muscle that generates force to pull the robot towards cancer cells in the direction of increasing acid concentration by varying activation strength differently in the horizontal and vertical planes. The precision is compared with other delivery methods. It was found that in a system with turbulence and blood pumping, the robot could deliver drugs to cancer cells more successfully than MOFs by 5.8 times at a pH operation range of 5.4, more than liposomes by 6.24 times at an operation range of 150 micrometers, and more than nanoparticles by 13.7 times at an operation range of 100 micrometers, confirming the successful design of both muscles that not only maintain stability but also enhance movement accuracy towards the target.

ABSTRACT. Magnetic Resonance Imaging (MRI) reconstruction remains a vital research domain, with ongoing efforts directed at enhancing image quality while minimizing acquisition time. Conventional k-space filling techniques have traditionally relied on Fourier transform properties and interpolation methods. However, recent innovations have introduced deep learning and compressed sensing as optimization strategies for this process. This study introduces a novel super-resolution framework that incorporates Toeplitz matrices for structured k-space completion, integrated with deep learning-based models and compressed sensing methodologies. Given their intrinsic connection to convolutional operations, Toeplitz matrices provide a mathematically sound foundation for defining k-space structures while ensuring data consistency.

Within this framework, deep neural networks are employed to infer the underlying k-space distribution in PROPELLER sequences from sparsely sampled data, while Toeplitz matrix constraints are utilized to maintain coherence. Additionally, the application of compressed sensing principles—incorporating sparsity priors and regularization techniques—improves both robustness and image quality, facilitating high-fidelity reconstructions from substantially undersampled acquisitions. The proposed approach is validated using both simulated and real MRI datasets, demonstrating that it effectively reduces reconstruction error and enhances image quality in comparison to traditional interpolation methods and standalone deep learning models. The findings indicate that combining sequentially rotating blade raw data acquisition with structured priors based on Toeplitz matrices, deep learning-driven inference, and compressed sensing optimization can yield more precise and computationally efficient MRI reconstructions, ultimately contributing to faster scan times in clinical applications.

ABSTRACT. Logistic regression with covariates is the gold standard for detecting epistasis (statistical genetic interactions) when analysing case-control datasets from genome-wide association studies (GWAS) of diseases. Nevertheless, genome-wide interaction studies (GWAIS) are still performed without covariate correction for performance reasons as the analysis of modern GWAS datasets may lead to several weeks of computation time. However, omitting necessary covariate information causes a substantial statistical error in most studies requiring genetic ancestry adjustment via principal component analysis (PCA), leading to an inflation in genome-wide test statistics and, thus, to non-replicable association results. Here, we present a novel approach that uses proxy covariates generated by k-means clustering in combination with contingency tables to reduce the runtime complexity of logistic regression from O(NI) to O(N+IK) and to minimize the statistical error compared to a ground truth (GT) implementation that uses per-sample covariate vectors from the PCA. Using GWAS data from 3,520 German patients with inflammatory bowel disease (IBD) and 4,288 healthy controls and a linkage disequilibrium (LD) pruned set of 141,621 genetic markers, we demonstrated a 97-fold speed-up with two k-means clusters from PCA covariates compared to the GT implementation using classical logistic regression with 10 PC covariates. At the same time, the mean relative error (MRE) was reduced by more than 55 %. Our developments enable logistic regression-based epistasis analysis with clustered PCA covariates for GWAS datasets on a genome-wide scale.

ABSTRACT. The paper addresses the optimization of dynamic circuits in quantum computing, with a focus on reducing the cost of mid-circuit measurements and resets. We extend the probabilistic circuit model (PCM) and implement an optimization framework that targets both mid-circuit measurements and resets. To overcome the limitation of the prior PCM-based pass, where optimizations are only possible on pure single-qubit states, we incorporate circuit synthesis to enable optimizations on multi-qubit states. With a parameter $n_{pcm}$, our framework balances optimization level against resource usage. We evaluate our framework using a large dataset of randomly generated dynamic circuits. Experimental results demonstrate that our method is highly effective in reducing mid-circuit measurements and resets. In our demonstrative example, when applying our optimization framework to the Bernstein-Vazirani algorithm after employing qubit reuse, we significantly reduce its runtime overhead by removing all of the resets.

ABSTRACT. Hybrid quantum algorithms combine the strengths of quantum and classical computing. Many quantum algorithms, such as the variational quantum eigensolver (VQE), leverage this synergy. However, quantum circuits are executed in full, even when only subsets of measurement outcomes contribute to subsequent classical computations. In this manuscript, we propose a novel circuit optimization technique that identifies and removes dead gates. We prove that the removal of dead gates has no influence on the probability distribution of the measurement outcomes that contribute to the subsequent calculation result. We implemented and evaluated our optimization on a VQE instance, a quantum phase estimation (QPE) instance, and random circuits, confirming its capability to remove a non-trivial number of dead gates in real-world algorithms. The effect of our optimization scales up as more measurement outcomes are identified as non-contributory, resulting in a proportionally greater reduction of dead gates.

ABSTRACT. Training of machine learning models consumes large amounts of energy. Since the energy consumption becomes a major problem in the development and implementation of artificial intelligence systems there exists a need to investigate the ways to reduce use of the resources by these systems. In this work we study how application of quantum annealers could lead to reduction of energy cost in training models aiming at pixel-level segmentation of hyperspectral images. Following the results of QBM4EO team, we propose a classical machine learning model, partially trained using quantum annealer, for hyperspectral image segmentation. We show that the model trained using quantum annealer is better or at least comparable with models trained using alternative algorithms, according to the preselected, common metrics. While direct energy use comparison does not make sense at the current stage of quantum computing technology development, we believe that our work proves that quantum annealing should be considered as a tool for training at least some machine learning models.

ABSTRACT. The recent advancements in noisy intermediate-scale quantum (NISQ) devices implementation allow us to study their application to real-life computational problems. However, hardware challenges are not the only ones that hinder our quantum computation capabilities. Software limitations are the other, less explored side of this medal. Using satellite image segmentation as a task example, we investigated how difficult it is to run a hybrid quantum-classical model on a real, publicly available quantum device. We also analyzed the costs of such endeavor and the change in quality of model.

ABSTRACT. The paper delves into the challenge of classification using dispersed data gathered from independent sources. The examined approach involves local models as ensembles of decision trees or random forests constructed based on local data. In the proposed model, a conflict analysis is used to identify the coalitions of local models. Two variants of forming coalitions were checked -- unified and diverse -- and two different strategies for generating final decisions were explored, allowing one or two of the strongest coalitions to make decisions. The diverse coalition approach is a wholly new and innovative strategy. The methods were tested and compared with corresponding accuracy-based weighted variants. The proposed approach improves classification performance, with weighted variants outperforming unweighted ones in balanced accuracy. Diverse model coalitions are especially effective for challenging and heterogeneous datasets.

ABSTRACT. In psychological research, network models are widely used to study symptoms of mental health disorders. However, these models often fail to account for uncertainty, leading to potentially misleading inferences. To address this issue, his study examines the robustness of psychological networks by analyzing a dataset on risk factors for suici- dal behavior with multiple network algorithms. We compare two causal discovery algorithms—Hill Climbing (HC) and TABU search—and the Gaussian Graphical Model (GGM), a widely used statistical network model in psychology. Uncertainty is assessed along two dimensions: (1) the impact of noise, by introducing varying levels of white noise into the dataset, and (2) the effect of sample size reduction, by systematically decreasing the number of observations. Our results indicate that both HC and TABU search are highly sensitive to noise and sample size, with HC slightly outperforming TABU in terms of precision and recall. GGM performance declines gradually with increasing noise and sample size reduction, leading to sparser networks. For all algorithms, recall declined at a faster rate than precision. Finally, we examine the robustness of edges leading to suicidal ideation, finding that the edge from Depression to suicide remains relatively stable across conditions. This is a promising result, since many suicide interventions are based on treating depressive mood. Our results emphasise the importance of considering uncertainty in network-based psychological research, particularly when applying causal discovery algorithms.

ABSTRACT. Precise determination of stellar parameters based on space telescope observations is a Big Data problem, which solving involves high-performance computing. After the solution is calculated, its quality should be assessed to determine its scientific value and, in case of issues, to indicate the ways towards its improvement. The tools for the solution quality assessment are as important as the solver itself and contribute to the solver’s tractability by unveiling the path to fine-tune the solving process. In our previous work, we created a high-performance astrometric solver AJAS suited for the Japan Astrometry Satellite Mission for INfrared Exploration (JASMINE). In the present work, we foster AJAS tractability by integrating it with the ontology-driven visual analytics platform SciVi leveraging the principles of multi-purpose ontology-driven API for in-situ data processing. This integration provides users with high-level management tools for AJAS computation jobs and high-level visual data mining tools for AJAS solutions. SciVi exposes a Web interface to the high-performance computing system and provides an intuitive visual programming language based on data flow diagrams allowing the users to describe the data processing pipelines from an extensible set of predefined operators. The composed pipelines can either be executed inside the SciVi environment or automatically converted to Jupyter Notebooks for further customisation in Python. In both cases, they are executed on the same computing resource as AJAS, which minimises the data transfer. To enable efficient access to the AJAS data from SciVi and Python, we developed a special data querying engine with a multithreaded C++ core and Python binding. We demonstrate our software capabilities with real examples of assessing the AJAS solution quality.

ABSTRACT. The exponential scaling of dataset volumes in contemporary deep learning imposes great computational and storage burdens across learning paradigms, which emphasizes the importance of intelligent dataset compression methods. Dataset distillation(DD) emerges as a promising solution for dataset size reduction. This study focus on the distribution matching framework for DD, introducing a novel methodology that quantifies the inter-distribution difference between source and distilled datasets via optimal transport theory, where Wasserstein metric $W_1$ serves as the discrepancy measurement. We implement this metric via the Kantorovich-Rubinstein(KR) dual $\sup_{f\in \text{Lip}(\Omega)}\mathbb{E}_{\mu_\mathcal{T}}[f] - \mathbb{E}_{\mu_\mathcal{S}}[f]$. According to Universal Approximation Theorem, a single-hidden-layer multilayer perceptron(MLP) with non-polynomial activation function can approximate continuous functions with arbitrary precise, thus a single-hidden-layer MLP is selected to approximate the function $f$ in the expression of KR dual while maintaining its Lipschitz continuity through a parameter truncation technique. Empirical evaluations demonstrate that our approach achieves performance comparable to the mainstream benchmarks. The empirical findings of this study validates the operational feasibility of employing Wasserstein distance and KR dual in DD problem. Related code is available at https://github.com/muyangli17/DD-with-KR-dual

ABSTRACT. The surge of retail investor activity on social media, exemplified by the 2021 GameStop short squeeze, raised questions about the influence of online sentiment on stock prices. This paper explores whether sentiment derived from social media discussions can meaningfully predict stock market movements. We focus on Reddit's r/wallstreetbets and analyze sentiment related to two companies: GameStop (GME) and AMC Entertainment (AMC). To assess sentiment's role, we employ two existing text-based sentiment analysis methods and introduce a third, a ChatGPT-annotated and fine-tuned RoBERTa-based model designed to better interpret the informal language and emojis prevalent in social media discussions. We use correlation and causality metrics to determine these models' predictive power. Surprisingly, our findings suggest that social media sentiment has only a weak correlation with stock prices. At the same time, simpler metrics, such as the volume of comments and Google search trends, exhibit stronger predictive signals. These results highlight the complexity of retail investor behavior and suggest that traditional sentiment analysis may not fully capture the nuances of market-moving online discussions. Future research should expand these analyses across different companies and time periods to refine sentiment-based stock market prediction models.

ABSTRACT. As modern IT infrastructures grow in complexity, root cause analysis (RCA) is becoming increasingly crucial for Site Reliability Engineering (SRE). Traditional RCA relies heavily on human expertise, making incident resolution time-consuming and error-prone. With the rise of AIOps (Artificial Intelligence for IT Operations), Large Language Models (LLMs) have emerged as potential tools for automating incident detection and diagnosis.

This study evaluates the capability of GPT-4o, Gemini-1.5, and Mistral-small in diagnosing system failures purely from observability metrics within a chaos engineering framework. We simulate eight real-world failure scenarios in a controlled e-commerce environment and assess LLMs' performance in zero-shot and few-shot settings compared with Site Reliability Engineers. While LLMs can identify common failure patterns, their accuracy is highly dependent on prompt engineering. In zero-shot settings, models achieve moderate accuracy (44–58\%), often misattributing harmless load spikes as security threats. However, few-shot prompting improves performance (60–74\% accuracy), suggesting that LLMs require structured guidance for reliable RCA.

Despite their potential, LLMs are not yet ready to replace human SREs, who achieved over 80\% accuracy due to hallucinations, misclassification biases, and lack of explainability. The findings highlight that LLMs can be co-pilots in incident response, but human oversight remains essential.

GitHub with code and dataset: \url{https://github.com/szandala/llms-chaos-engineering}

ABSTRACT. Group B Streptococcus (GBS) remains a leading cause of neonatal mortality, underscoring the need for effective vaccination strategies. This study presents a computational model that simulates the immune response to the Type V GBS capsular polysaccharide-tetanus toxoid (GBS-TT) conjugate vaccine, calibrated and validated against clinical cohort data. The model, based on a system of ordinary differential equations (ODEs) adapted from a previous framework, was optimized using Differential Evolution (DE) to reproduce antibody dynamics for both unconjugated (37$\mu$g CPS) and conjugated (9.6$\mu$g CPS/4.3$\mu$g TT) vaccines. The calibrated model accurately replicated dose-dependent antibody titers across four formulations, including higher(38.5$\mu$g CPS/17.0$\mu$g TT) and lower (2.4$\mu$g CPS/1.1$\mu$g TT) doses. Notably, key parameters- specifically, the antigen-presenting cell maturation rate and the antibody-mediated vaccine clearance rate- were 93-fold and 1,700-fold higher, respectively, in conjugated vaccines compared to unconjugated formulations, reflecting the adjuvant effect of tetanus toxoid in enhancing immunity.

ABSTRACT. This study presents a computational model that simulates the human immune response to SARS-CoV-2, validated using data from multiple studies. The model tracks the temporal evolution of mature CD4+ T cells, mature CD8+ T cells, viruses, and antibodies across three COVID-19 severity scenarios: mild, severe, and critical. In the mild scenario, results closely align with observed data, particularly for T lymphocytes. In the severe scenario, the model accurately reproduces virus and antibody dynamics but exhibits some deviation in mature CD8+ T cells behavior. For the critical scenario, while mature CD4+ T cells and antibodies align well with literature data, discrepancies arise in virus and CD8+ T cell dynamics. Despite these variations, all model-generated curves remain within significant portions of the data’s confidence intervals, demonstrating the model’s qualitative ability to capture immune response trends across different disease severities.

ABSTRACT. Blood cell analysis is an important part of assessing health and immunity. White blood cells (WBCs), or leukocytes, play an important role in immune responses, including inflammation, allergic reactions, protection against infections, or even against cancer. Accurate recognition and counting of WBCs make it possible to early detect various conditions. Traditional methods are time-consuming and costly, pushing research toward the development of advanced automated solutions. This study proposes a deep Convolutional Neural Network (CNN) for automated recognition and classification of five WBC types from microscopic images. Various network structures, filter sizes, numbers of hidden layers, and different learning algorithms were evaluated to achieve high accuracy. In this way, {$18$} network variants, including different learning algorithms, were tested. Several of them achieved very high accuracy in recognizing and scoring {$5$} types of WBCs. The efficiency of the proposed models can be used to help medical professionals, offering potential support in enhancing diagnostic efficiency and blood analysis.

ABSTRACT. The increasing accessibility of next-generation sequencing (NGS) techniques has significantly expanded transcriptomics research. However, this expansion has led to major computational challenges due to the amount volume of data generated. BioSkel is a framework designed to facilitate the development of bioinformatics workflows for transcriptomics, offering both flexibility and parallelization for shared-memory and distributed-memory architectures. BioSkel allows bioinformaticians to tailor data processing pipelines by integrating custom code while abstracting parallelization complexities. This paper presents new experimental results demonstrating BioSkel’s applicability to real-world clinical transcriptomic studies. We show that BioSkel achieves alignment accuracy comparable to state-of-the-art tools while offering scalable performance on distributed architectures. These results highlight the framework’s potential for dealing with large-scale transcriptomics data processing.

ABSTRACT. This study investigates the impact of variations in the frequency factor ($A$) and activation energy ($E_a$) on the Arrhenius model for tissue damage assessment in hyperthermia cancer treatment. A three-dimensional breast tissue model was employed to perform uncertainty quantification using Monte Carlo simulations, treating $A$ and $E_a$ as probability density functions. Numerical results indicate that variations in $A$ have a minor influence on tissue damage, while changes in $E_a$ significantly affect thermal damage progression. Notably, uncertainty in $E_a$ leads to a broad confidence interval for the critical damage threshold ($\Omega \geq 4$), causing the required time to reach this threshold to range from 15 to 35 minutes.

ABSTRACT. Quantum Machine Learning (QML) has emerged as a promising field at the intersection of quantum computing and Machine Learning (ML), offering new possibilities for enhanced data processing and classification tasks. In particular, quantum kernel methods have demonstrated potential advantages over their classical counterparts in high-dimensional feature mapping. In the transition toward more sustainable energy, Power Quality Disturbance (PQD) classification is crucial for ensuring grid stability amid growing renewable energy integration. Rapid and accurate detection of disturbances enables timely corrective actions to maintain reliable power supply. Support Vector Machines (SVMs), a class of supervised ML models based on kernel methods, have been widely used for PQD classification due to their strong generalization capabilities. In this paper, we integrate a quantum approach into the SVM framework and propose a novel quantum-classical dual kernel SVM that outperforms both purely classical and purely quantum kernel SVMs on an S-transform PQD dataset. By incorporating a weighting strategy between classical and quantum kernels, we develop a robust and highly accurate PQD classification model, achieving an average accuracy of 98.46% across all noise levels. To the best of our knowledge, this is the first application of a quantum-classical dual kernel SVM in power system applications, thereby demonstrating QML’s potential to enhance real-world classification.

ABSTRACT. The problem of data classification realized by the convolutional networks, although successfully implemented using classical methods, is also important in the area of quantum networks and is subject to continuous development and research. In this work, we present an example of classification for a set of higher dimensionality than the currently used solutions based on the MNIST or FASHION databases. Additionally, we show that working on raw data not transformed by, for example, PCA reduction or other advanced classical pre-processing techniques, very high classification quality can be achieved also without using any hybrid techniques. In the discussed solution, classification is performed by checking whether the obtained final state, or more precisely the probability distribution of the basis states superposition, is consistent with the appropriate state representing the given label. This comparison can be carried out using basic techniques such as Kullback–Leibler divergence or SWAP-Test, especially if we want the classification process to be realized solely in the quantum computation model without using any post-processing with classical techniques.

ABSTRACT. We consider a graph labeling problem, i.e., the cyclic bandwidth problem, and its formulation in QUBO, the input language for quantum computers based on quantum annealing. To this end, we first consider a constraint programming model based on table constraints and then we derive from this model the QUBO formulation and its penalty matrix. We also detail an analysis of this QUBO model in terms of number of qubits and their required inter-qubit connections in order to estimate the suitability of implementing such a solution on quantum annealers, i.e., the D-Wave Advantage system with a specific graph topology for qubit couplers.

ABSTRACT. This study explores a formalised dynamical systems model of the General Escape Theory of Suicide using Sobol and PAWN global sensitivity analyses. The findings highlight the importance of self-feedback loops, the effect of stressors on aversive internal states, and the inter- action effects between aversive internal states and the urge to escape on suicidal ideation and non-suicidal escape behaviours. Time-dependent sensitivity analysis also reveals the long-term stability of parameter importance over time. These results hold potential for informing clinical interventions by identifying the most important influences for individual suicidal ideation.

ABSTRACT. The paper describes a multidimensional approach to solving a fuzzy complex linear system (FCLS). Together with the definition of arithmetic operations on complex fuzzy numbers with a horizontal granular membership function, the properties of these basic arithmetic operations are given and proven. Using the horizontal membership function of the fuzzy number and its counterpart in the complex number space, a multidimensional full granule of solution of FCLS was obtained. There are many methods in the scientific literature that generate results that are not full solutions of FCLS. The examples presented show that the use of the horizontal approach generates a full solution and indicate differences with the results obtained from other methods cited in the article. Furthermore, with granular approach the solution of the full FCLS was calculated.

ABSTRACT. When an operational parameter presents extremely high variability, uncertainty becomes extreme. Long-tail probability distributions can be used to model such uncertainty. We present a queuing system in which extreme uncertainty is modelled using long-tail probability distributions. There have been many queuing analyses for a single server queue fed by an M/G/traffic process, in which G is a Pareto distribution, that focus on certain limiting conditions. In this paper, we present a mathematical model to solve an infinite queuing system with one server where the inter-arrival time between jobs follows a Pareto probability distribution with shape parameter α and a scale parameter A. The system service time is also a Pareto probability distribution with shape parameter β and scale parameter B. We call this the P/P/1 queuing model

ABSTRACT. Linear elasticity and Navier-Stokes equations are fundamental tools in material science, enabling the modeling of solid deformations and fluid flows under various conditions. These equations are widely used to simulate stresses, strains, and fluid interactions in processes like 3D printing, welding, casting, and extrusion. Physics-Informed Neural Networks (PINNs), introduced in 2019, have gained significant attention for solving complex physical problems, including fluid mechanics, wave propagation, and inverse problems. Despite their growing popularity, PINNs face challenges in training efficiency and accuracy. This paper investigates the applicability of modern PINN methodologies to material science problems involving Navier-Stokes and linear elasticity equations. For linear elasticity, a randomized selection of collocation points is employed to enhance training. For Navier-Stokes equations, hard constraints on initial and boundary conditions are implemented to avoid multi-objective optimization. These approaches aim to address training difficulties and improve PINN performance in simulating material science phenomena.

ABSTRACT. The Edge-Strength (ES) problem is a graph labeling problem where the goal is to assign integer labels to the edges of a finite undirected graph in such a way that the maximum sum of labels between any two adjacent edges, known as edge-strength, is minimized. This work introduces the first methods to solve the \es~problem exactly and approximately, including two constraint satisfaction problem (CSP) models and a simulated annealing (SA) metaheuristic. The first CSP model is based on constrained optimization using the AllDifferent global constraint, while the second employs extensional constraints. Computational experiments on 40 standard topology graph instances demonstrate the effectiveness and robustness of these approaches. The CSP models provide exact solutions for smaller instances, while the SA algorithm efficiently approximates solutions for larger and complex graphs. These contributions advance the state-of-the-art in solving the ES problem and pave the way for further research.

ABSTRACT. Fitting Gaussian Mixture Models (GMMs) to one-dimensional data is a fundamental task in machine learning, traditionally addressed using the Expectation-Maximization (EM) algorithm. However, EM lacks inherent mechanisms to enforce separation between mixture components, a critical requirement in domains like medical research where distinct subgroups must be identified. Recently, the Distribution Optimization (DO) framework addressed this limitation by reformulating GMM estimation as a chi-squared goodness-of-fit minimization problem with an overlap penalty to enhance separation. However, its reliance on equiwidth binning and genetic algorithms can limit accuracy and scalability. In this paper, we refine the DO framework in two key ways: (1) replacing equiwidth binning with Mann–Wald's equiprobable cells to improve estimation accuracy, and (2) adopting advanced Differential Evolution (DE) for more robust optimization of the high-dimensional parameter space. Through extensive experiments on synthetic and real-world datasets, we demonstrate that our refined approach significantly enhances accuracy, stability, and scalability compared to the original DO method.

ABSTRACT. The problem of fitting reduced data Qm is discussed here. The latter forms the ordered sequanece of interpolation pointts. in arbitrary Euclidean space. Here the corresponding interpolation knots are replaced with new ones compensated by the so called exponential parameterization determied by reduced data and a single parameter running over [0,1]. In sequel, a modified complete spline is used to interpolate Q- with the aid of exponential parameterization. The main theoretical contribution of this work is to prove a linear convergence order in curve estimation by fitting Q- woth modified complete spline based on exponential parameterization for parameter in [0,1). The latter holds for sufficiently smooth, regular curve sampled more-or-less uniformly. The asymptotics established here is subsequently verified numerically in affirmative as sharp. The respective tests are conducted on 2D and 3D curves.