All cyclic Steiner triple systems of order 45 (STS(45)s) have been known since 1980. Their point-cyclic resolutions possess a cyclic automorphism group of order 45 and were classified recently. In the present paper we consider a next open problem. We construct the resolutions of the cyclic STS(45)s which are invariant under the subgroup of order 15 of the cyclic automorphism group of order 45. We succeed to solve this problem using the high-performance computing system Avitohol. We also establish if the constructed resolutions possess some additional properties which are important for possible applications to different kinds of LDPC codes and erasure-resilient codes for large disk arrays.
The performance of algorithmic trading strategies, especially those based on Volume Spread Analysis (VSA), is strongly dependent on the selection and adjustment of critical parameters. This study uses Monte Carlo sensitivity analysis (SA) to determine how modifications in these factors affect trading performance. The method dynamically reacts to market conditions using a rolling window of 168 candles, with volume as an independent variable and price spread as a dependent variable, to provide predictive signals. Sensitivity analysis shows that profit-target and stop-loss settings have the greatest influence on strategy outcomes, followed by volume threshold and moving average periods. A Pareto frontier analysis shows the trade-offs between maximizing returns and minimizing drawdowns, providing insight into the best parameter settings. The findings show that adjusting these parameters improves strategy resilience, increasing risk-adjusted returns while retaining profitability. The findings highlight the need for systematic adjustment of the parameters in the development of the trading algorithm. Incorporating sensitivity analysis improves the consistency of trading performance in across market scenarios.
The increasing dependence on information technology in many aspects of human life often causes high demand for resources, in particular energy, which has an impact on the environment obeying natural, physical limita-tions. Global sustainability requires efficient responsible computing and im-provement of hardware and software energy efficiency. This article focuses of software energy efficiency and its role towards sustainable computing. The introduction points out Bremermann’s limit and the possible conse-quences if extensive improvements in computing performance approach this limit. The role of energy-efficient software applied to large-scale tasks is ana-lysed. An empirical study illustrates the energy efficiency of different algo-rithms when solving identical large-scale numerical tests. A brief discussion and consideration of further work conclude the article.
Cyclotides are cyclic peptides exhibiting remarkable stability due to their cyclic cystine knot (CCK) motif, making them attractive scaffolds for drug design. However, their structural integrity under varying physiological conditions remains an important consideration for therapeutic development. In this study, we investigate the pH-dependent conformational dynamics of the trypsin-inhibitor cyclotide MCoTI-I using constant pH molecular dynamics (CpHMD) simulations. We simulated the cyclotide at different pH, ranging from 1 to 9, tracking protonation states, titration behavior, and conformational fluctuations of ionizable residues. While basic residues remained predominantly protonated, dynamic protonation-deprotonation events were observed for three aspartic acid residues. Notably, Asp ^16 exhibited a significant downward pKa shift, attributed to its limited solvent accessibility and stabilizing interactions with nearby arginines. Structural analyses revealed pH-sensitive loop dynamics. These findings underscore the importance of studying protonation-coupled flexibility in the context of rational design of stable grafted peptide aptamer therapeutics based on cyclotide scaffolds.
We propose and investigate space-time discontinuous Galerkin (DG) finite element approximations of the wave equation that is recast as an evolutionary first-order system. The DG gradient and DG divergence operator on broken polynomial spaces are defined carefully. The solution of the algebraic system by GMRES iterations with geometric multigrid (GMG) preconditioning is addressed. The performance properties of the DG approach are illustrated by numerical experiments.
A neural network-based technique for monitoring the structural health of beams is developed and presented. The aim of the work is to define and train a neural network that is able to localize damages and to estimate their severity. Training data is generated by numerical simulations based on Timoshenko’s beam theory. The transverse displacements are obtained by numerically solving the equation of motion for various damage locations, damages of varying severities, and excitation frequencies. The results demonstrate that the neural network accurately identifies the location and severity of damage, even under noisy conditions.
Climate change and the socio-economic transformations have significantly increased the frequency and intensity of forest fires in European countries in the last 30 years. Traditional methods of monitoring and extinguishing forest fires often do not have the tools to predict the development of a given fire, which in some cases leads not only to economic losses, but also to human casualties. Bulgaria although its modest size is having breaking records burned areas and number of fires for the year of 2024 in comparison with the period 1970–2023. In such dynamic environmental changes, decision support tools that can support data collection, data validation and optimization of the decision making processes are crucial. Meteorological conditions, detailed terrain information and vegetation types affected in cases of ignition are the first and basic parameters, that the responsible authorities are looking for. Thus in our article will be presented a pilot web-based tool which is available freely on-line for five test zones in the municipal areas of Kresna, Zlatograd, Svilengrad, Haskovo and Topolovgrad. The tool is part of the decision support instruments in the five municipalities and provide in real time, data from local meteorological stations, GIS information for terrain, vegetation, water resources and evacuation safe zones.
Sobol and Halton sequences are well-known low-discrepancy sequences used in numerical simulations. Compared to pseudorandom numbers, they offer superior uniformity, making them useful for numerical integration, optimization, and high-dimensional modelling. In practice, these sequences are often scrambled to improve their statistical properties and enable error estimation. There are various scrambling methods, each with different computational costs, implementation complexities, and levels of uniformity. Moreover, both Sobol and Halton sequences can be generated using skip and leap parameters, which further influence their statistical behaviour. In this paper, we investigate the influence of skip and leap parameters on scrambled Sobol and Halton sequences when estimating the maximum eigenvalue of a covariance matrix. Since the covariance matrix is vital for portfolio risk management, its largest eigenvalue offers key insights into concentration and overall risk. The estimation is carried out using the Almost Optimal Power Quasi-Monte Carlo (PQMC) algorithm on annual data from a 32-asset portfolio. Results show that incorporating the skip and leap parameters enables PQMC to strike a balance between systematic and stochastic errors, reducing computational effort while maintaining a fixed error tolerance. Conversely, omitting these parameters requires greater computational resources to achieve similar accuracy.
Air pollution is of big concern in many countries, despite different measures taken by the local authorities. The meteorological and chemical-transport models capabilities depend on many factors, as the descriptions of their physics, dynamics, chemical transformations and spatial-temporal grid resolutions. The implications emerging from these properties are important for the robust interpretation of the model results, which in turn influences the final decisions concerning the air quality in specific city, country, or region as a whole. The current study concerning the processes determining the Ozone ( O_3 ). The O_3 is important not only in troposphere, but also in the stratosphere. The stratospheric Ozone in the Earth’s atmosphere is formed under the influence of solar radiation and is distributed under the influence of atmospheric dynamics. Stratospheric ozone forms a protective layer that protects the Earth’s biosphere from the harmful effects of ultraviolet solar radiation in the 280–315 nm range. Variations in this ozone layer are caused by seasonal changes in atmospheric dynamics, particularly stratospheric warming. The current study focused only the surface O_3 in Bulgaria, according to previous results show that this pollutant are among the ones that are responsible for the most frequent episodes of air quality deterioration in both urban and rural sites. The main goal of that research is to display the effect of grid size of the emissions and process description on the different mechanisms responsible for the concentration of O_3 over Bulgaria. For that purpose, a system of three models was used: meteorological, emission and chemical-transport model (WRF, SMOKE and CMAQ). The numerical experiments for different cases indicated the lead impact of the grid resolution on the concentrations and the dynamical and chemical processes contribution on the concentrations. The presented results in the paper display that, for simulation of the atmospheric composition, the grid and the source description resolution play a significant role.
Natural and anthropogenic disasters have happened ever since the dawn of time and human history. Thousands of people have lost their lives or have suffered different health impairments due to disasters like earthquakes, floods, volcanic eruptions, military conflicts, acts of terrorism, chemical and nuclear accidents, etc. Nevertheless, some social groups are particularly vulnerable in such extreme situations. In such groups, the number of casualties and victims is noticeably and disproportionally bigger in comparison with the total number of the population affected. In fact, it seems that the social status differences are most clearly visible in disaster situations. The purpose of this research is to identify such vulnerable groups in our society, with the aim of organizing advance preparation actions with regard to improving prevention and minimizing the aftermath, the number of victims and the effects of natural or manmade disasters among such groups. We propose the use of cluster analysis to divide people into groups of susceptibility.
Image processing techniques play an important role in tasks such as denoising, segmentation, and analysis of diverse image datasets. In this paper, we will investigate the computational aspects of a combined multi-stage PDE-based image processing approach. This approach consists of three stages: image formation, noise filtering, relying upon nonlinear diffusion, and image segmentation. These stages can be combined into one nonlinear optimisation problem which is then solved using the alternating direction method of multipliers (ADMM). We evaluate the performance of the method using a 3D MR image.
We propose an extension of the Greedy Sampling Neural Network SINDy (GN-SINDy) methodology for learning systems influenced by an external control input (excitation). The proposed method builds on the existing approach of combining neural networks with the SINDy approach for identifying partial differential equations using a greedy sampling approach. The application of interest is a catalytic CO_2 methanation reactor, for which the dynamics are described by highly complex coupled equations. The quantities of interest are the temperature and CO_2 conversion. We show that the proposed method effectively fits predictive surrogate models in sparse format, i.e., described by only a few terms, while incorporating the influence of control inputs.
Trust is a fundamental force that binds society together, yet the emergence and evolution of collective trust in social groups remain insufficiently understood. With over two billion active users engaging online, vast amounts of data provide an opportunity to analyze trust formation at a large scale. In this work, we integrate high-performance data analytics of empirical data to investigate how the structure of social networks influences trust dynamics. We aim to uncover key network properties that drive collective trust by leveraging complex network theory and novel topological methods. We explain our approach in details and apply it to one of the closed social groups in Stack Exchange networks. Our results show that while this group had relatively large and well connected core, typical for sustainable communities, the dynamics of collective trust was a good indicator of its dissolution. We illustrate how different types of structures contribute to the dynamics of the number of active users and the role of collective trust in the sustainability of online social groups.
In this work uncertainty quantification for reactive transport through random porous media is considered. Such problems are of scientific and practical interest. Steady-state two-dimensional Darcy equation for computing the pressure, coupled to convection-reaction-diffusion equation describing the reactive transport. Both equations are with random coefficients. The applicability and superiority of MLMC method for solving such problems with a huge parametric space are demonstrated. The coarse grain strategies used for constructing the MLMC model are discussed. Lognormal distribution for the permeability is considered, based on numerous experimental observations.
This work presents recent advances in modeling and solving linear poroelasticity problems, with a specific application to the Tunnel Sealing Experiment conducted in an underground research laboratory. The motivation for this work is to estimate the material parameters of the rock massif using experimental data, employing a Bayesian inversion framework enhanced by surrogate models. This framework necessitates evaluating thousands of instances of the forward poroelastic model with varying material parameters. The poroelastic model, implemented in FEniCSx, incorporates pore pressure and displacement dynamics governed by Biot’s equations. It is discretized using the finite element method in space and the implicit Euler method in time. Efficient solution of this model is crucial for the effective application of the Bayesian framework. To achieve this, we employed block preconditioners to solve time step problems with heterogeneous parameters. These were combined with deflated Krylov methods, which exploit similarities between solutions at successive time steps. The use of these techniques significantly accelerated computations, allowing for the evaluation of more samples and ultimately leading to a more accurate estimation of the physical parameters.
Live performances offer unique opportunities to captivate audiences by blending artistic expression with technological innovation. By introducing advanced tools such as Machine Learning and Generative AI, the visual dimension of performances can be transformed to provide more immersive and emotionally resonant experiences. In one of our earlier research, we developed an integrated hardware and software framework to enhance live performances by dynamically combining performer visuals with AI-generated backgrounds. Our approach used robotic cameras in a master-slave configuration to track and analyze performers in real time. The master camera processes video data to identify the number of subjects, analyzes their facial expressions, and determines emotional states using deep learning techniques. These emotional cues influenced both the selection of a performer for projection and the generation of a tailored visual background. While our prior work suggested sentiment analysis as a key criterion for performer selection, the broader development of a comprehensive selection model and the exploration of additional criteria and scenarios were left as future directions. In this article, we go further our prior work by introducing a novel actor selection model inspired by the adaptive behavior of wasps. This bio-inspired algorithm evaluates multiple dynamic criteria, including emotional analysis, movement patterns, and contribution to the performance, to optimize the selection of performers for projection onto AI-generated visuals. Our proposed model leverages multiple parameters to generate diverse scenarios for performer selection, adapting to real-time changes in single and multi-actor settings, such as concerts, opera, theater, dance and choral performances.
Tensor contraction operation occurs in many applications of tensor networks. Optimal tensor contraction is generally NP-hard. One particular type of tensor network is the tensor train. We show that tensor train contraction is a generalization of matrix chain multiplication from bi-dimensional to multi-dimensional matrices. We propose a polynomial dynamic programming algorithm for optimal tensor train contraction and we present its theoretical analysis.
Quantum computing has attracted significant attention, partially due to the potential to achieve significant speedups in diverse optimization tasks. Quantum Machine Learning aims to utilize quantum computations as part of the workflow, in my cases resulting in hybrid methods. Kernel methods are well studied approach in problems for classification or regression, where kernels are employed to deal with non-linearity in the data. Kernels that use quantum circuits have been considered, and some theoretical or practical results have been achieved. As we have the flexibility to choose how to construct the basic quantum circuit to be used, the question is how to dynamically build a circuit that is sufficiently adapted to the dataset. In this work we propose a novel algorithm that uses genetic algorithms for this task, while also employing a neural network in order to speed-up the evolutionary process by attempting to predict the accuracy of the kernel method when using a candidate circuit. We describe in detail the algorithm and provide numerical examples using widely known datasets that show the performance that can be obtained. We demonstrate that the method is viable and produces results that are comparable to other established prediction algorithms, with wide potential for further improvement.
We consider a Henry-like intrusion problem, where fluid flow is driven by variations in fluid density. The Multi-Level Monte Carlo (MLMC) method is employed to estimate the mean value of a quantity of interest (QoI). The QoI is defined as the earliest time at which the mass fraction of salt exceeds a given threshold. In our setting, porosity, permeability, recharge, and fracture thickness are treated as uncertain parameters and modeled as random variables. For each realization of these parameters, the evolution of the salt mass fraction is governed by a system of nonlinear, time-dependent partial differential equations (PDEs). We demonstrate that the MLMC method can be effectively applied to this problem, significantly reducing computational costs compared to classical Monte Carlo methods. The findings of this study have the potential to enhance and accelerate the monitoring of drinking water resources and pollution dynamics.
Objective methods for assessing the welfare of farm animals are sought on a global scale, in order to compare the well-being of animals reared under different conditions. The aim of this study was to create a mathematical model for animal welfare assessment of lambs during different periods. Using the model, we compared the welfare of lambs in the experimental and control groups mathematically, and determined the effect of the food additive - Silymarin (2 g/kg feed) on the improvement of their welfare. The complex method is based on the scientific concept of the five freedoms that guarantee animal welfare, given by the Animal Welfare Council of Great Britain (FAWC, 1995). Each of the five freedoms was assessed on a 5-point scale, depending on its degree of manifestation in lambs. The assessment of each of the freedoms was determined based on statistically significant changes in the behavior of the lambs, in the levels of corticosterone and serotonin between the control and experimental groups. Using a mathematical model, the welfare of the control lambs was estimated at AW control = 50.50
