Computation

This article examines the possibilities of adapting approximate solutions of boundary value problems for differential equations using physics-informed neural networks (PINNs) to changes in data about the physical entity being modelled. Two types of models are considered: PINN and parametric PINN (PPINN). The former is constructed for a fixed parameter of the problem, while the latter includes the parameter for the number of input variables. The models are tested on three problems. The first problem involves modelling the bending of a cantilever rod under varying loads. The second task is a non-stationary problem of a thermal explosion in the plane-parallel case. The initial model is constructed based on an ordinary differential equation, while the modelling object satisfies a partial differential equation. The third task is to solve a partial differential equation of mixed type depending on time. In all cases, the initial models are adapted to the corresponding pseudo-measurements generated based on changing equations. A series of experiments are carried out for each problem with different functions of a parameter that reflects the character of changes in the object. A comparative analysis of the quality of the PINN and PPINN models and their resistance to data changes has been conducted for the first time in this study. Full article

The aim of this study is to develop a physical model and investigate the bactericidal effect of an automated hand-washing system through numerical computation, which is essential in areas affected by COVID-19 to ensure safety and limit the spread of the pandemic. The computational fluid dynamics approach is used to study the movement of the solution inside the hand-washing chamber. The finite element method with the k-$\epsilon$ model is applied to solve the incompressible Navier–Stokes equations. The numerical results provide insights into the solution’s hydrodynamic values, streamlines, and density in the two cases of with a hand and without a hand. The pressure and mean velocity of the fluid in the hand-washing chamber increases when the inlet flow rates increase. When the hand-washing chamber operates, it creates whirlpools around the hands, which remove bacteria. In addition, the liquid inlet flow affects the pressure in the hand-washing chamber. The ability to predict the hydraulic and cleaning performance efficiencies of the hand-washing chamber is crucial for evaluating its operability and improving its design in the future. Full article

The article presents the development of new physics-informed evolutionary neural network learning algorithms. These algorithms aim to address the challenges of ill-posed problems by constructing a population close to the Pareto front. The study focuses on comparing the algorithm’s capabilities based on three quality criteria of solutions. To evaluate the algorithms’ performance, two benchmark problems have been used. The first involved solving the Laplace equation in square regions with discontinuous boundary conditions. The second problem considered the absence of boundary conditions but with the presence of measurements. Additionally, the study investigates the influence of hyperparameters on the final results. Comparisons have been made between the proposed algorithms and standard algorithms for constructing neural networks based on physics (commonly referred to as vanilla’s algorithms). The results demonstrate the advantage of the proposed algorithms in achieving better performance when solving incorrectly posed problems. Furthermore, the proposed algorithms have the ability to identify specific solutions with the desired smoothness. Full article

A numerical investigation of masonry walls subjected to blast loads is presented in this article. A non-linear finite element model is proposed to describe the structural response of the walls. A unilateral contact–friction law is used in the interfaces of the masonry blocks to provide the discrete failure between the blocks. A continuum damage plasticity model is also used to account for the compressive and tensile failure of the blocks. The main goal of this article is to investigate the different collapse mechanisms that arise as an effect of the blast load parameters and the static load of the wall. Parametric studies are conducted to evaluate the effect of the blast source–wall (standoff) distance and the blast weight on the structural response of the system. It is shown that the traditional in-plane diagonal cracking failure mode may still dominate when a blast action is present, depending on the considered standoff distance and the blast weight when in-plane static loading is also applied to the wall. It is also highlighted that the presence of an opening in the wall may significantly reduce the effect of the blasting action. Full article

The diffusion kinetics theory of cleaning assemblies such as combustion engines with flushing oil has been introduced. Evolution of tar deposits on the engine surfaces and in the lube system has been described through the erosion dynamics. The time-dependent concentration pattern related to hydrodynamic (sub)layers around the tar deposit has been uncovered. Nonlinear equations explaining the experimentally observed dependences for scouring the contaminants off with the oil have been derived and indicate the power law in time. For reference purposes, a similar analysis based on formal chemical kinetics has been accomplished. Factors and scouring parameters for the favor of either mechanism have been discussed. Any preference for either diffusion or chemical kinetics should be based on a careful selection of washing agents in the flushing oil. Future directions of studies are proposed. Full article

A quadrotor trajectory tracking problem is addressed via the design of a model reference adaptive control (MRAC) system. As for real-world applications, the entire quadrotor dynamics is typically unknown. To take that into account, we consider a plant model, which contains uncertain nonlinear terms resulting from aerodynamic friction, blade flapping, and the fact that the mass and inertia moments of the quadrotor may change from their nominal values. Unlike many known studies, the explicit equations of the parameter uncertainty for the position control loop are derived in two different ways using the differential flatness approach: the control signals are (i) used and (ii) not used in the parametric uncertainty parameterization. After analysis, the neural network (NN) is chosen for both cases as a compensator of such uncertainty, and the set of NN input signals is justified for each of them. Unlike many known MRAC systems with NN for quadrotors, in this study, we use the $k_{x}x+k_{r}r$ baseline controller, which follows from the control system derivation, with both time-invariant (parameterization (i)) and adjustable (parameterization (ii)) parameters instead of an arbitrarily chosen non-tunable PI/PD/PID-like one. Adaptive laws are derived to adjust the parameters of NN uncertainty compensator for both parameterizations. As a result, the position controller ensures the asymptotic stability of the tracking error for both cases under the assumption of perfect attitude loop tracking, which is ensured in the system previously developed by the authors. The results of the numerical experiments support the theoretical conclusions and provide a comparison of the effectiveness of the derived parameterizations. They also allow us to make conclusions on the necessity of the baseline controller adjustment. Full article

The complexity (number of spanning trees) in a finite graph $\Gamma$ (network) is crucial. The quantity of spanning trees is a fundamental indicator for assessing the dependability of a network. The best and most dependable network is the one with the most spanning trees. In graph theory, one constantly strives to create novel structures from existing ones. The super subdivision operation produces more complicated networks, and the matrices of these networks can be divided into block matrices. Using methods from linear algebra and the characteristics of block matrices, we derive explicit formulas for determining the complexity of the super subdivision of a certain family of graphs, including the cycle $C_n$, where $n=3,4,5,6$; the dumbbell graph $D{b}_{m,n}$; the dragon graph $P_m\left(C_n\right)$; the prism graph ${\Pi }_n$, where $n=3,4$; the cycle $C_n$ with a $P_{\frac{n}{2}}$-chord, where $n=4,6$; and the complete graph $K_4$. Additionally, 3D plots that were created using our results serve as illustrations. Full article

Visible light positioning systems (VLP) have attracted significant commercial and research interest because of the many advantages they possess over other applications such as radio frequency (RF) positioning systems. In this work, an experimental configuration of an indoor VLP system based on the well-known Lambertian light emission, is investigated. The corresponding results are also presented, and show that the system retains high enough accuracy to be operational, even in cases of low transmitted power and high background noise. Full article

We present a numerical platform for 3D imaging and general analysis of multidimensional complex THz fields. A special 3D visualization is obtained by converting electromagnetic (EM) radiation to a light field via the Wigner distribution function, which is known for discovering (revealing) hidden details. This allows for 3D diagnostics using the simple techniques of geometrical optics, which significantly facilitates the whole analysis. This simulation was applied to a complex field composed of complex beams emitted as ultra-narrow femtosecond pulses. A method was developed for the generation of phase–amplitude and spectral characteristics of complex multimode radiation in a free-electron laser (FEL) operating under various parameters. The tool was successful at diagnosing an early design of the transmission line (TL) of an innovative accelerator at the Schlesinger Family Center for Compact Accelerators, Radiation Sources, and Applications. Full article

The construction of a mathematical model of a complicated system is often associated with the evaluation of inputs’ (arguments, factors) influence on the output (response), the identification of important relationships between the variables used, and reduction of the model by decreasing the number of its inputs. These tasks are related to the problems of Sensitivity Analysis of mathematical models. The author proposes an alternative approach based on applying Analysis of Finite Fluctuations that uses the Lagrange mean value theorem to estimate the contribution of changes to the variables of a function to the output change. The article investigates the presented approach on an example of a class of fully connected neural network models. As a result of Sensitivity Analysis, a set of sensitivity measures for each input is obtained. For their averaging, it is proposed to use a point-and-interval estimation algorithm using Tukey’s weighted average. The comparison of the described method with the computation of Sobol’s indices is given; the consistency of the proposed method is shown. The computational robustness of the procedure for finding sensitivity measures of inputs is investigated. Numerical experiments are carried out on the neuraldat data set of the NeuralNetTools library of the R data processing language and on data of the healthcare services provided in the Lipetsk region. Full article

Background: In present genomes, current relics of a circular RNA appear which could have played a central role as a primitive catalyst of the peptide genesis. Methods: Using a proximity measure to this circular RNA and the distance, a new unsupervised classifier called Maxwell^TM has been constructed based on the Burrows–Wheeler transform algorithm. Results: By applying the classifier to numerous genomes from various realms (Bacteria, Archaea, Vegetables and Animals), we obtain phylogenetic trees that are coherent with biological trees based on pure evolutionary arguments. Discussion: We discuss the role of the combinatorial operators responsible for the evolution of the genome of many species. Conclusions: We opened up possibilities for understanding the mechanisms of a primitive factory of peptides represented by an RNA ring. We showed that this ring was able to transmit some of its sub-sequences in the sequences of genes involved in the mechanisms of the current ribosomal production of proteins. Full article

The Reissner–Nordstrom spacetimes and some generalised Reissner–Nordstrom spacetimes are analysed. The blackhole solutions are considered. The generalised Reissner–Nordstrom spacetimes with a cosmological-constant term, endowed with a Schwarzschild solid-angle element, are analytically delineated: the radii of the blackholes are analytically calculated and newly parameterised; the coordinate-singularity-avoiding coordinate extension is newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the new conditions for merging the solutions as the physical horizons are analytically outlined; the new parameter space of the model is set and constrained; the new role of the cosmological-constant term in designating the Schwarzschild radius is demonstrated; the Reissner–Nordstrom–deSitter case and in the Reissner–Nordstrom–anti-deSitter one are newly demonstrated to be characterised in a different analytical manner. Furthermore, a new family of solutions is found, qualified after the cosmological-constant term. The generalised Reissner–Nordstrom spacetimes with a linear term, endowed with a Schwarzschild solid-angle element, are analytically studied: the radii are enumerated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are set; the new parameter space of the system is arranged and constrained; the role of the linear-term parameter in the delineation of the Schwarzschild radius is newly proven to be apt to imply a small modification only. The generalised Reissner–Nordstrom spacetimes, endowed with a Schwarzschild solid-angle element, with a linear term and a cosmological-constant term are newly inspected: the radii are analytically calculated and newly parameterised; the new conditions for the merging of the radii as the physical horizons are prescribed; the new parameter space of the scheme is appointed and constrained; the roles of the parameters are newly scrutinised in their application to modify the physical interpretation of the Reissner–Nordstrom parameters only in a small manner; the coordinate-singularity-avoiding coordinate extensions are newly found, i.e., such that the tortoise-coordinate transformation can therefore be applied; the definition of the physical radii is newly found; the results are newly demonstrated in both cases of a positive value of the cosmological constant and in the case of a negative value of the cosmological constant in a different manner; the role of the linear-term parameter is also newly enunciated. More over, a new family of solutions is found, which is delineated after particular values of the linear term and of the cosmological-constant one. The quantum implementation of the models is prospectively envisaged. Full article

Cryptocurrencies are rapidly growing and are increasingly accepted by major commercial vendors. However, along with their rising popularity, they have also become the go-to currency for illicit activities driven by the anonymity they provide. Cryptocurrencies such as the one on the Ethereum blockchain provide a way for entities to hide their real-world identities behind pseudonyms, also known as addresses. Hence, the purpose of this work is to uncover the level of anonymity in Ethereum by investigating multiclass classification models for Externally Owned Accounts (EOAs) of Ethereum. The researchers aim to achieve this by examining patterns of transaction activity associated with these addresses. Using a labelled Ethereum address dataset from Kaggle and the Ethereum crypto dataset by Google BigQuery, an address profiles dataset was compiled based on the transaction history of the addresses. The compiled dataset, consisting of 4371 samples, was used to tune and evaluate the Random Forest, Gradient Boosting and XGBoost classifier for predicting the category of the addresses. The best-performing model found for the problem was the XGBoost classifier, achieving an accuracy of 75.3% with a macro-averaged F1-Score of 0.689. Following closely was the Random Forest classifier, with an accuracy of 73.7% and a macro-averaged F1-Score of 0.641. Gradient Boosting came in last with 73% accuracy and a macro-averaged F1-Score of 0.659. Owing to the data limitations in this study, the overall scores of the best model were weaker in comparison to similar research, with the exception of precision, which scored slightly higher. Nevertheless, the results proved that it is possible to predict the category of an Ethereum wallet address such as Phish/Hack, Scamming, Exchange and ICO wallets based on its transaction behaviour. Full article

At present, fuzzy modeling has established itself as an effective tool for designing and developing systems for various purposes that are used to solve problems of control, diagnostics, forecasting, and decision making. One of the most important problems is the choice and justification of an appropriate functional representation of the main fuzzy operations. It is known that, in the class of rational functions, such operations can be represented by additive generators in the form of a linear fractional function, a logarithm of a linear fractional function, and an arctangent of a linear fractional function. The paper is devoted to the latter case. Restrictions on the parameters, under which the arctangent of a linear fractional function is an increasing or decreasing generator, are defined. For each case, a corresponding fuzzy operation (a triangular norm or a conorm) is constructed. The theoretical significance of the research results lies in the fact that the obtained parametric families enrich the theory of Archimedean triangular norms and conorms and provide additional opportunities for the functional representation of fuzzy operations in the framework of fuzzy modeling. In addition, in fact, we formed a scheme for study functions that can be considered additive generators and constructed the corresponding fuzzy operations. Full article

In this work, we present a new way of studying the mathematical structure of the genetic code. This study relies on the use of mathematical computations involving five Fibonacci-like sequences; a few of their “seeds” or “initial conditions” are chosen according to the chemical and physical data of the three amino acids serine, arginine and leucine, playing a prominent role in a recent symmetry classification scheme of the genetic code. It appears that these mathematical sequences, of the same kind as the famous Fibonacci series, apart from their usual recurrence relations, are highly intertwined by many useful linear relationships. Using these sequences and also various sums or linear combinations of them, we derive several physical and chemical quantities of interest, such as the number of total coding codons, 61, obeying various degeneracy patterns, the detailed number of H/CNOS atoms and the integer molecular mass (or nucleon number), in the side chains of the coded amino acids and also in various degeneracy patterns, in agreement with those described in the literature. We also discover, as a by-product, an accurate description of the very chemical structure of the four ribonucleotides uridine monophosphate (UMP), cytidine monophosphate (CMP), adenosine monophosphate (AMP) and guanosine monophosphate (GMP), the building blocks of RNA whose groupings, in three units, constitute the triplet codons. In summary, we find a full mathematical and chemical connection with the “ideal sextet’s classification scheme”, which we alluded to above, as well as with others—notably, the Findley–Findley–McGlynn and Rumer’s symmetrical classifications. Full article

We consider the multispecies model described by a coupled system of diffusion–reaction equations, where the coupling and nonlinearity are given in the reaction part. We construct a semi-discrete form using a finite volume approximation by space. The fully implicit scheme is used for approximation by time, which leads to solving the coupled nonlinear system of equations at each time step. This paper presents two uncoupling techniques based on the explicit–implicit scheme and the operator-splitting method. In the explicit–implicit scheme, we take the concentration of one species in coupling term from the previous time layer to obtain a linear uncoupled system of equations. The second approach is based on the operator-splitting technique, where we first solve uncoupled equations with the diffusion operator and then solve the equations with the local reaction operator. The stability estimates are derived for both proposed uncoupling schemes. We present a numerical investigation for the uncoupling techniques with varying time step sizes and different scales of the diffusion coefficient. Full article

Information is transmitted between multiple insecure routing hops in text, image, video, and audio. Thus, this multi-hop digital data transfer makes secure transmission with confidentiality and integrity imperative. This protection of the transmitted data can be achieved via hashing algorithms. Furthermore, data integrity must be ensured, which is feasible using hashing algorithms. The advanced cryptographic Secure Hashing Algorithm 3 (SHA-3) is not sensitive to a cryptanalysis attack and is widely preferred due to its long-term security in various applications. However, due to the ever-increasing size of the data to be transmitted, an effective improvement is required to fulfill real-time computations with multiple types of optimization. The use of FPGAs is the ideal mechanism to improve algorithm performance and other metrics, such as throughput (Gbps), frequency (MHz), efficiency (Mbps/slices), reduction of area (slices), and power consumption. Providing upgraded computer architectures for SHA-3 is an active area of research, with continuous performance improvements. In this article, we have focused on enhancing the hardware performance metrics of throughput and efficiency by reducing the area cost of the SHA-3 for all output size lengths (224, 256, 384, and 512 bits). Our approach introduces a novel architectural design based on pipelining, which is combined with a simplified format for the round constant (RC) generator in the Iota ($\iota$) step only consisting of 7 bits rather than the standard 64 bits. By reducing hardware resource utilization in the area and minimizing the amount of computation required at the Iota ($\iota$) step, our design achieves the highest levels of throughput and efficiency. Through extensive experimentation, we have demonstrated the remarkable performance of our approach. Our results showcase an impressive throughput rate of 22.94 Gbps and an efficiency rate of 19.95 Mbps/slices. Our work contributes to advancing computer architectures tailored for SHA-3, therefore unlocking new possibilities for secure and high-performance data transmission. Full article

Knee osteoarthritis is a musculoskeletal defect specific to the soft tissues in the knee joint and is a degenerative disease that affects millions of people. Although drug intake can slow down progression, total knee arthroplasty has been the gold standard for the treatment of this disease. This surgical procedure involves replacing the tibiofemoral joint with an implant. The most common implants used for this require the removal of either the anterior cruciate ligament (ACL) alone or both cruciate ligaments which alters the native knee joint mechanics. Bi-cruciate-retaining implants have been developed but not frequently used due to the complexity of the procedure and the occurrences of intraoperative failures such as ACL and tibial eminence rupture. In this study, a knee joint implant was modified to have a bone graft that should aid in ACL reconstruction. The mechanical behavior of the bone graft was studied through finite element analysis (FEA). The results show that the peak Christensen safety factor for cortical bone is 0.021 while the maximum shear stress of the cancellous bone is 3 MPa which signifies that the cancellous bone could fail when subjected to the ACL loads, depending on the graft shear strength which could vary depending on the graft source, while cortical bone could withstand the walking load. It would be necessary to optimize the bone graft geometry for stress distribution as well as to evaluate the effectiveness of bone healing prior to implementation. Full article

Extreme flooding of the floodplains of large lowland rivers poses a danger to the population due to the vastness of the flooded areas. This requires the organization of safe evacuation in conditions of a shortage of temporary and transport resources due to significant differences in the moments of flooding of different spatial parts. We consider the case of a shortage of evacuation vehicles, in which the safe evacuation of the entire population to permanent evacuation points is impossible. Therefore, the evacuation is divided into two stages with the organization of temporary evacuation points on evacuation routes. Our goal is to develop a method for analyzing the minimum resource requirement for the safe evacuation of the population of floodplain territories based on a mathematical model of flood dynamics and minimizing the number of vehicles on a set of safe evacuation schedules. The core of the approach is a numerical hydrodynamic model in shallow water approximation. Modeling the hydrological regime of a real water body requires a multi-layer geoinformation model of the territory with layers of relief, channel structure, and social infrastructure. High-performance computing is performed on GPUs using CUDA. The optimization problem is a variant of the resource investment problem of scheduling theory with deadlines for completing work and is solved on the basis of a heuristic algorithm. We use the results of numerical simulation of floods for the Northern part of the Volga-Akhtuba floodplain to plot the dependence of the minimum number of vehicles that ensure the safe evacuation of the population. The minimum transport resources depend on the water discharge in the Volga river, the start of the evacuation, and the localization of temporary evacuation points. The developed algorithm constructs a set of safe evacuation schedules for the minimum allowable number of vehicles in various flood scenarios. The population evacuation schedules constructed for the Volga-Akhtuba floodplain can be used in practice for various vast river valleys. Full article