Network intrusion detection in non-stationary traffic is complicated by concept drift and class imbalance. This study presents an Adaptive Incremental Random Forest (AIRF) update policy that combines selective tree retention, attack-ratio-based buffering with bounded deferral, and a validation-based quality gate. The framework is evaluated on the CSE-CIC-IDS2018 benchmark in its original temporal order. For accepted training/update events, the F1-score ranges from 0.9149 to 1.0000, with a mean of 0.9873. Separately, the iteration-3 candidate obtains an F1-score of 0.5118 and is rejected by the gate; the subsequent merged 3+4 update obtains an F1-score of 0.9994. The experiment demonstrates the intended update-control behavior on one benchmark and one reported run. Accordingly, these results are interpreted as proof-of-concept evidence rather than evidence of statistical superiority or cross-dataset generalization.
In this work, we consider a time-dependent convection-diffusion problem in a heterogeneous medium. The fine-grid approximation is constructed using the finite element method with an implicit time scheme. For the coarse-scale approximation, we apply the Meshfree Generalized Multiscale Finite Element Method (Meshfree GMsFEM), in which local computations are performed on subdomains associated with a point cloud instead of a structured coarse grid. Two approaches to the construction of the subdomains and the corresponding kernel functions are compared. In the first approach, the subdomains are Euclidean balls and the kernel functions are radially symmetric. In the second approach, the subdomains are geodesic balls in an anisotropic metric induced by the convective velocity field, and the kernel functions are constructed using an ellipsoidal distance adapted to the subdomain geometry, with a transition layer whose width is proportional to the coarse scale. Multiscale basis functions are obtained by the solution of local spectral problems in snapshot spaces that take into account the convective term. Numerical results are presented for two model problems with different boundary conditions and velocity fields. For approximately the same average number of fine-grid cells per subdomain, the transport-adapted construction provides smaller relative L2 errors and H1-seminorm errors for all considered dimensions of the coarse space.
In this paper, we study a time-optimal control problem for the heat equation on a right isosceles triangular domain with Dirichlet boundary conditions. The control function appears as a distributed source term, and the objective is to steer the system from the zero initial state to a prescribed weighted temperature level in the shortest possible time under a unit amplitude constraint. Using spectral decomposition, the problem is reduced to a Volterra integral equation of the first kind whose kernel is shown to be positive and continuous. Under nonnegativity assumptions on the actuator profile and the weight function, an explicit upper bound for the minimal time is derived in terms of the smallest eigenvalue and the corresponding Fourier coefficients. The results illustrate how the spectral properties of the triangle influence the controllability of the system.
Linear systems resulting from power flow analysis using the Newton-Raphson method are challenging due to their large size, sparsity structure and bad conditioning. Iterative Krylov subspace techniques such as Bi-Conjugate Gradient (BICG) and its variants GPBICG and BICGSTAB are commonly used to accelerate convergence. Alternatives such as Bi-Conjugate Residual (BICR) and its variants GPBICR and BICRSTAB for solving power flow problems recently emerged in the numerical linear algebra literature exhibiting promising stability and convergence properties. In this work we asses the suitability of BICRSTAB and GPBICR for solving power flow problems. We perform numerical experiments encompassing a range of size and condition number on several test cases chosen from the MATPOWER library. The two solvers are compared with the BICGSTAB and GPBICG algorithms using several criteria including CPU time and number of iterations to achieve convergence. Our results demonstrate that BICR variants outperform traditional BICG variants in specific situations, suggesting they are a good attractive for simulating power flows problems.
This work studies the application of the topological derivative method for the detection and characterization of inclusions in materials using elastic waves. It presents a simplified mathematical model for elastic wave propagation in materials with embedded defects like inclusions or cavities. This model is subsequently employed to generate synthetic data used to test and validate the topological derivative method. The tests explore a range of parameters related to the materials and configurations of multiple inclusions, as well as to the generation of the elastic waves, with the aim of assessing their impact on the performance of the topological derivative method. The main objective is to determine whether the method can detect multiple simultaneous inclusions made of different materials, distinguish them based on their constituent materials, and infer the properties of each inclusion. A set of numerical experiments addressing these issues is presented, emphasizing both the capabilities and the limitations of the topological derivative method.
