Shodhan Rao

Arjan van der Schaft, Shodhan Rao, Bayu Jayawardhana

Motivated by recent progress on the interplay between graph theory, dynamics, and systems theory, we revisit the analysis of chemical reaction networks described by mass action kinetics. For reaction networks possessing a thermodynamic equilibrium we derive a compact formulation exhibiting at the same time the structure of the complex graph and the stoichiometry of the network, and which admits a direct thermodynamical interpretation. This formulation allows us to easily characterize the set of equilibria and their stability properties. Furthermore, we develop a framework for interconnection of chemical reaction networks. Finally we discuss how the established framework leads to a new approach for model reduction.

Shodhan Rao, Arjan van der Schaft, Bayu Jayawardhana

In this paper we derive a compact mathematical formulation describing the dynamics of chemical reaction networks that are complex-balanced and are governed by mass action kinetics. The formulation is based on the graph of (substrate and product) complexes and the stoichiometric information of these complexes, and crucially uses a balanced weighted Laplacian matrix. It is shown that this formulation leads to elegant methods for characterizing the space of all equilibria for complex-balanced networks and for deriving stability properties of such networks. We propose a method for model reduction of complex-balanced networks, which is similar to the Kron reduction method for electrical networks and involves the computation of Schur complements of the balanced weighted Laplacian matrix.

Shodhan Rao, Arjan van der Schaft, Karen van Eunen et al.

In this paper we propose a model-order reduction method for chemical reaction networks governed by general enzyme kinetics, including the mass-action and Michaelis-Menten kinetics. The model-order reduction method is based on the Kron reduction of the weighted Laplacian matrix which describes the graph structure of complexes in the chemical reaction network. We apply our method to a yeast glycolysis model, where the simulation result shows that the transient behaviour of a number of key metabolites of the reduced-order model is in good agreement with those of the full-order model.

Utku Ozbulak, Manvel Gasparyan, Shodhan Rao et al.

Predictions made by deep neural networks were shown to be highly sensitive to small changes made in the input space where such maliciously crafted data points containing small perturbations are being referred to as adversarial examples. On the other hand, recent research suggests that the same networks can also be extremely insensitive to changes of large magnitude, where predictions of two largely different data points can be mapped to approximately the same output. In such cases, features of two data points are said to approximately collide, thus leading to the largely similar predictions. Our results improve and extend the work of Li et al.(2019), laying out theoretical grounds for the data points that have colluding features from the perspective of weights of neural networks, revealing that neural networks not only suffer from features that approximately collide but also suffer from features that exactly collide. We identify the necessary conditions for the existence of such scenarios, hereby investigating a large number of DNNs that have been used to solve various computer vision problems. Furthermore, we propose the Null-space search, a numerical approach that does not rely on heuristics, to create data points with colliding features for any input and for any task, including, but not limited to, classification, localization, and segmentation.