Related papers: Complex-linear invariants of biochemical networks
The prediction of physicochemical properties from molecular structures is a crucial task for artificial intelligence aided molecular design. A growing number of Graph Neural Networks (GNNs) have been proposed to address this challenge.…
Computer algebra methods for analyzing reaction networks often rely on the assumption of mass-action kinetics, which transform the governing ODEs into polynomial systems amenable to techniques such as Gr\"obner basis computation and related…
The set of functions parameterized by a linear fully-connected neural network is a determinantal variety. We investigate the subvariety of functions that are equivariant or invariant under the action of a permutation group. Examples of such…
Solving the intricate quantum behavior of interacting particles is key to unlocking the mysteries of condensed matter, but capturing their complex correlations across different scales remains a monumental challenge. We introduce a neural…
Chemical reaction network theory is a field of applied mathematics concerned with modeling chemical systems, and can be used in other contexts such as in systems biology to study cellular signaling pathways or epidemiology to study the…
Molecular computation based on chemical reaction networks (CRNs) has emerged as a promising paradigm for designing programmable biochemical systems. However, the implementation of complex computations still requires excessively large and…
Recent years have witnessed a hot wave of deep neural networks in various domains; however, it is not yet well understood theoretically. A theoretical characterization of deep neural networks should point out their approximation ability and…
Systematic relations between multiple objects that occur in various fields can be represented as networks. Real-world networks typically exhibit complex topologies whose structural properties are key factors in characterizing and further…
Predicting monomer reactivity ratios is crucial for controlling monomer sequence distribution in copolymers and their properties. Traditional experimental methods of determining reactivity ratios are time-consuming and resource-intensive,…
A detailed understanding of biochemical networks at the molecular level is essential for studying complex cellular processes. In this paper, we provide a comprehensive description of biochemical networks by considering individual atoms and…
This work addresses whether a reaction network, taken with mass-action kinetics, is multistationary, that is, admits more than one positive steady state in some stoichiometric compatibility class. We build on previous work on the effect…
A major challenge in network science is to determine parameters governing complex network dynamics from experimental observations and theoretical models. In complex chemical reaction networks, for example, such as those describing processes…
Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for…
A large variety of dynamical systems, such as chemical and biomolecular systems, can be seen as networks of nonlinear entities. Prediction, control, and identification of such nonlinear networks require knowledge of the state of the system.…
Dynamical systems arising from chemical reaction networks with mass action kinetics are the subject of chemical reaction network theory (CRNT). In particular, this theory provides statements about uniqueness, existence, and stability of…
Biochemical covalent modification networks exhibit a remarkable suite of steady state and dynamical properties such as multistationarity, oscillations, ultrasensitivity and absolute concentration robustness. This paper focuses on conditions…
Under mass-action kinetics, biochemical reaction networks give rise to polynomial autonomous dynamical systems whose parameters are often difficult to estimate. We deal in this paper with the problem of identifying the kinetic parameters of…
We propose an end-to-end deep learning learning model for graph classification and representation learning that is invariant to permutation of the nodes of the input graphs. We address the challenge of learning a fixed size graph…
Model reduction of biochemical networks relies on the knowledge of slow and fast variables. We provide a geometric method, based on the Newton polytope, to identify slow variables of a biochemical network with polynomial rate functions. The…
Chemical reaction networks (CRNs) are a standard formalism used in chemistry and biology to reason about the dynamics of molecular interaction networks. In their interpretation by ordinary differential equations, CRNs provide a…