Direct Determination of Reduced Models of a Class of Singularly Perturbed Nonlinear Systems on Three Time Scales in a Bond Graph Approach

One of the most important features in the analysis of the singular perturbation methods is the reduction of models. Likewise, the bond graph methodology in dynamic system modeling has been widely used. In this paper, the bond graph modeling of nonlinear systems with singular perturbations is presented. The class of nonlinear systems is the product of state variables on three time scales (fast, medium, and slow). Through this paper, the symmetry of mathematical modeling and graphical modeling can be established. A main characteristic of the bond graph is the application of causality to its elements. When an integral causality is assigned to the storage elements that determine the state variables, the dynamic model is obtained. If the storage elements of the fast dynamics have a derivative causality and the storage elements of the medium and slow dynamics an integral causality is assigned, a reduced model is obtained, which consists of a dynamic model for the medium and slow time scales and a stationary model of the fast time scale. By applying derivative causality to the storage elements of the fast and medium dynamics and an integral causality to the storage elements of the slow dynamics, the quasi-steady-state model for the slow dynamics is obtained and stationary models for the fast and medium dynamics are defined. The exact and reduced models of singularly perturbed systems can be interpreted as another symmetry in the development of this paper. Finally, the proposed methodology was applied to a system with three time scales in a bond graph approach, and simulation results are shown in order to indicate the effectiveness of the proposed methodology.

Modeling and analyzing predictive monthly survival in females diagnosed with gynecological cancers

Cancer ranks as a leading cause of death worldwide; an estimated 1.7 million new diagnoses were reported in 2021. Ovarian cancer, the most lethal of gynecological malignancies, has no effective screening with over 70% of patients being diagnosed in an advanced stage. The aim of this study was to determine the most statistically significant contributing factors through a multivariate regression into the severity of female gynecological cancers. Data from the surveillance, epidemiology, and end results program (SEER) cancer database were utilized in this study. Several attempted multivariate linear regressions were implemented with further reduced models; however, a linear model could not be properly fit to the data. Because of unmet assumptions, a nonparametric moving, local regression, locally estimated scatterplot smoothing (LOESS), was performed. After smoothing factors were included to reduced-models, residual information was minimized although few conclusions can be drawn from the resulting statistics. These issues were prevalent mainly because of the massive variability in the data and inherent lack of linearity. This can be a significant issue with clinical data that does not dive deeper into cancer-dependent factors including genetic expression and cell surface receptor overexpression. General patient demographic data and diagnostic information alone does not provide enough detail to make a definite conclusion or prediction on patient survivability. Increased attention to the acquisition of tumor tissue for genomic and proteomic analysis in addition to next-generation sequencing methods can lead to significant improvements in prognostic predictions.

A structural property for reduction of biochemical networks

Large-scale biochemical models are of increasing sizes due to the consideration of interacting organisms and tissues. Model reduction approaches that preserve the flux phenotypes can simplify the analysis and predictions of steady-state metabolic phenotypes. However, existing approaches either restrict functionality of reduced models or do not lead to significant decreases in the number of modelled metabolites. Here, we introduce an approach for model reduction based on the structural property of balancing of complexes that preserves the steady-state fluxes supported by the network and can be efficiently determined at genome scale. Using two large-scale mass-action kinetic models of Escherichia coli, we show that our approach results in a substantial reduction of 99% of metabolites. Applications to genome-scale metabolic models across kingdoms of life result in up to 55% and 85% reduction in the number of metabolites when arbitrary and mass-action kinetics is assumed, respectively. We also show that predictions of the specific growth rate from the reduced models match those based on the original models. Since steady-state flux phenotypes from the original model are preserved in the reduced, the approach paves the way for analysing other metabolic phenotypes in large-scale biochemical networks.

Testing of the new JOREK stellarator-capable model in the tokamak limit

In preparation for extending the JOREK nonlinear magnetohydrodynamics (MHD) code to stellarators, a hierarchy of stellarator-capable reduced and full MHD models has been derived and tested. The derivation was presented at the EFTC 2019 conference. Continuing this line of work, we have implemented the reduced MHD model (Nikulsin et al., Phys. Plasmas, vol. 26, 2019, 102109) as well as an alternative model which was newly derived using a different set of projection operators for obtaining the scalar momentum equations from the full MHD vector momentum equation. With the new operators, the reduced model matches the standard JOREK reduced models for tokamaks in the tokamak limit and conserves energy exactly, while momentum conservation is less accurate than in the original model whenever field-aligned flow is present.