Computational and Mathematical Methods

We prove the equivalence of two-symbol supersaturated designs (SSDs) with (even) rows, columns, and , where and and resolvable incomplete block designs (RIBDs) whose any two blocks intersect in at most points. Using this equivalence, we formulate the search for two-symbol -optimal and minimax-optimal SSDs with as a search for RIBDs whose blocks intersect accordingly. This allows developing a bit-parallel tabu search (TS) algorithm. The TS algorithm found -optimal and minimax-optimal SSDs achieving the sharpest known lower bound with of sizes , (16, 26), (16, 27), (18, 23), (18, 24), (18, 25), (18, 26), (18, 27), (18, 28), (18, 29), (20, 21), (22, 22), (22, 23), (24, 24), and (24, 25). In each of these cases, no such SSD could previously be found.

In this article, we have carried out a case study to optimize the classification of the maliciousness of cybersecurity events by IP addresses using machine learning techniques. The optimization is studied focusing on time complexity. Firstly, we have used the extreme gradient boosting model, and secondly, we have parallelized the machine learning algorithm to study the effect of using a different number of cores for the problem. We have classified the cybersecurity events’ maliciousness in a biclass and a multiclass scenario. All the experiments have been carried out with a well-known optimal set of features: the geolocation information of the IP address. However, the geolocation features of an IP address can change over time. Also, the relation between the IP address and its label of maliciousness can be modified if we test the address several times. Then, the models’ performance could degrade because the information acquired from training on past samples may not generalize well to new samples. This situation is known as concept drift. For this reason, it is necessary to study if the optimization proposed works in a concept drift scenario. The results show that the concept drift does not degrade the models. Also, boosting algorithms achieving competitive or better performance compared to similar research works for the biclass scenario and an effective categorization for the multiclass case. The best efficient setting is reached using five nodes regarding high-performance computation resources.

In this study, we examined the impact of Cu-H₂O nanoparticles on two-dimensional Casson nanofluid flows past permeable stretching/shrinking sheet embedded in a Darcy-Forchheimer porous medium in the presence of slipperiness of surface, suction/injection, viscous dissipation, and convective heating. Using some realistic assumptions and appropriate similarity transformations, the governing nonlinear partial differential equations were formulated and transformed into a system of nonlinear ordinary differential equations and then numerically solved by using the shooting technique. Numerical results are displayed for dimensionless fluid velocity and temperature profiles, skin friction, and the local Nusselt number. The impacts of different governing physical parameters on these quantities are presented and discussed using graphs, tables, and a chart. For the specific range of shrinking sheet, the result shows that dual solutions exist, and temporal stability analysis is performed by introducing small disturbances to determine the stable solutions. It is detected that the upper branch solution is hydrodynamically stable and substantially realistic; however, the lower branch solution is unstable and physically unachievable. The fluid flow stability is obtained by enhancing the suction, surface slipperiness, and viscous dissipation parameters. However, augmenting the values of the Casson factor, Cu-H₂O nanoparticle volume fraction, porous medium, porous medium inertia, and convective heating parameters increases the blow-up stability of the fluid flow. The rate of heat transfer enhances with the increment in the Casson factor, porous medium, porous medium inertia, suction, velocity ratio, nanoparticle volume fraction, and convective heating parameters, whereas it reduces as the slipperiness of the surface and viscous dissipation parameters rise. Increment of Cu-H₂O nanoparticle volume fraction into the Casson fluid boosts the heat transfer enhancement rate higher for the shrinking sheet surface.

Physical laws provide a mathematical description of a physical phenomenon. The mathematical description is generally in the form of differential equations with appropriate initial and boundary conditions, called initial boundary value problems. The dimensionless form of an initial boundary value problem is the first step for the solution to a class of problems. The approach is generally applied for closed-form (or analytical) solutions, whereas practical engineering problems can only be solved numerically. Commercial finite element packages are commonly used for the numerical solution of engineering problems with complexities caused by geometry, loading, and material properties. A numerical solution does not produce a formula; therefore, a completely new solution must be obtained even for minor changes in the data set. A single-dimensionless finite element analysis would solve a class of problems. Literature shows that user-developed finite element codes, not accessible for general use, are generally used for dimensionless finite element solutions. The availability of dimensionless analysis in a commercial finite element package would be very convenient. Commercial packages do not have built-in dimensionless formulations. However, all mainstream packages allow user-implemented formulation through different coding requirements. At least one researcher has used a commercial package for dimensionless analyses without coding. The work presents a guide on alternate implementation methods of dimensionless formulations in commercial packages. A sample case demonstrates the stepwise implementation of a dimensionless formulation without writing a customized finite element code.

A directed Toeplitz graph with vertices , , , is a directed graph whose adjacency matrix is a Toeplitz matrix. In this paper, we investigate the Hamiltonicity in directed Toeplitz graphs with and .

The data on SARS-CoV-2 (COVID-19) in South Africa show seasonal transmission patterns to date, with the peaks having occurred in winter and summer since the outbreaks began. The transmission dynamics have mainly been driven by variations in environmental factors and virus evolution, and the two are at the center of driving the different waves of the disease. It is thus important to understand the role of seasonality in the transmission dynamics of COVID-19. In this paper, a compartmental model with a time-dependent transmission rate is formulated and the stabilities of the steady states analyzed. We note that if , the disease-free equilibrium is globally asymptotically stable, and the disease completely dies out; and when , the system admits a positive periodic solution, and the disease is uniformly or periodically persistent. The model is fitted to data on new cases in South Africa for the first four waves. The model results indicate the need to consider seasonality in the transmission dynamics of COVID-19 and its importance in modeling fluctuations in the data for new cases. The potential impact of seasonality in the transmission patterns of COVID-19 and the public health implications is discussed.