Abstract This study demonstrates the potential of several methods for analysing the sensitivity of neural networks to perturbations of the input data and for interpreting their underlying mechanisms. The approaches investigated include Sobol global sensitivity analysis, local sensitivity analysis for input-pixel perturbations and the activation maximisation technique. As examples, we consider a small feedforward neural network for analysing an open tabular dataset of clinical diabetes data, as well as two classical convolutional architectures, VGG-16 and ResNet-18, which are widely used in image processing and classification. The use of global sensitivity analysis allows us to identify the leading input parameters of the chosen tiny neural network and to reduce their number without significant loss of accuracy. Since global sensitivity analysis is not applicable to larger models, we apply local sensitivity analysis and activation maximisation to the convolutional neural networks. These methods reveal interesting patterns for the convolutional models solving the image classification problem. Overall, we compare the results of activation maximisation with the popular Grad-CAM technique in the context of ultrasound data analysis.
Abstract The architecture of the lymphatic system (LS) is a critical factor determining the nature of immune responses. We reconstructed and compared the topological graphs of the murine LS in wild-type (WT) mice [D. Grebennikov et al., Network modeling of murine lymphatic system, Algorithms 16 (2023), No. 3, 168]and in a recombinant inbred mouse line with the lpr mutation (RM) characterised by swollen lymph nodes (MXH10/Mo- lpr / lpr ) [A. Sukhbaatar et al., Lymphatic topology reveals a novel intranodal lympho-venous shunt, The Journal of Pathology 268 (2026), No. 4, 477–492].The WT LS graph contained 88 nodes (27 lymph nodes) and 87 directed edges; the RM LS graph comprised 99 nodes (42 lymph nodes) and 113 edges. Common groups of lymph nodes (popliteal, subiliac, mediastinal, etc.) were identified, and, in addition, each data set contained node labels that could not be matched between the two graphs; these unmatched labels may reflect true anatomical variation or differences in nomenclature and dissection detail. The RM LS network is characterised by a larger number of sources, a larger spectral radius, and a greater maximum degree, indicating significant topological remodelling of the LS associated with the lpr mutation. The results provide a quantitative basis for modelling immune cell trafficking and biochemical species transfer in genetically modified mice.
Abstract A stochastic model of contact cytolysis in the innate immune response has been constructed. The duration of contact cytolysis is determined by a distribution function concentrated on a finite time interval. The model variables include the sizes of populations of viral particles and cells of several types, families of unique types of latently infected cells, and complexes formed by productively infected cells and NK cells. The theories of discontinuous Markov processes and branching random processes are used to construct and study the model. The results of computational experiments with the model based on the Monte Carlo method are presented. Conditions for the completion or development of the infectious process over a finite time interval are studied numerically.
Abstract We propose a quasi-potential Newton-type solver for nonlinear algebraic systems, with applications to equilibrium problems in finite-strain biomechanics. The nonlinear operator is decomposed into the gradient of a local energy functional and a remainder determined by the skew-symmetric part of its Jacobian. In mechanics, the functional is equal to the negative work of the total nodal forces along linear trajectories. The resulting potential-skew splitting enables local energy minimisation to serve as a globalisation mechanism even for non-conservative systems. Local convergence to the solution is established under conditions relating the coercivity of the symmetric Jacobian part to the magnitude and variation of its skew part. The solver combines regularised Newton minimisation, admissibility control, Newton acceleration, and adaptive pseudo-time continuation. Numerical experiments on seven volumetric and shell-contact biomechanical problems show superior performance compared with line-search and regularised Newton methods, reducing the number of function evaluations by factors of 2–23 and wall time by factors of 1.3–17.7.
Abstract The principal result is a strong partitioned time-integration algorithm for a class of coupled dynamical models whose subsystems are advanced by independent time integrators and interact through a finite-dimensional vector of interface variables. Each coupling trial recomputes both subsystem trajectories from the converged state at t n , evaluates the interface data at the internal stage times required by each solver, and advances the complete coupled state only after convergence of the interface fixed point. The general construction permits different discretisations for subsystems with different mathematical structure, while its applicability requires well-posed subsystem propagators and a locally convergent relaxed interface iteration. The algorithm is specialised to a closed-loop zero-dimensional–one-dimensional cardiovascular model. Cardiac chambers are described by 0D inertial-resistive pressure-volume relations with time-dependent elastance, the valves by a smooth damped second-order model, the major vessels by 1D hyperbolic balance laws, and the peripheral circulations by two-compliance blocks. The chamber-valve differential-algebraic system is integrated by a one-stage, two-derivative, third-order Obreshkov formula. The vascular discretisation combines MUSCL reconstruction, the local Rusanov flux, second-order compatibility conditions, and an IMEX–SSP2(2, 2, 2) method. A short banded pulmonary artery segment is represented by a passive dynamic interface. Dynamic relaxation reduces the mean number of subsystem trials from 8.71 to 2.58 and the maximum from 37 to 5, corresponding to a reduction of approximately 70% in this direct cost measure. Component tests verify the automatic differentiation, compatibility conditions, finite-volume and IMEX discretisations, band solver, and volume balance. Adult and neonatal four-chamber calculations are compared with published physiological ranges. A neonatal three-chamber model then quantifies the dependence of pulmonary-to-systemic flow, distal pulmonary pressure, systemic cardiac index, proximal loading, and dynamic pressure loss on the relative band diameter. Patient-specific use requires clinical calibration and additional representation of oxygen transport and congenital shunts.
