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We propose an abstract framework for analyzing the convergence of least-squares methods based on residual minimization when feasible solutions are neural networks. With the norm relations and compactness arguments, we derive error estimates…
The Turing completeness of continuous chemical reaction networks (CRNs) states that any computable real function can be computed by a continuous CRN on a finite set of molecular species, possibly restricted to elementary reactions, i.e.…
Predicting stochastic cellular dynamics as emerging from the mechanistic models of molecular interactions is a long-standing challenge in systems biology: low-level chemical reaction network (CRN) models give raise to a highly-dimensional…
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…
Step Chemical Reaction Networks (step CRNs) are an augmentation of the Chemical Reaction Network (CRN) model where additional species may be introduced to the system in a sequence of ``steps.'' We study step CRN systems using a weak subset…
In recent years, deep learning methods have been successfully applied to single-image super-resolution tasks. Despite their great performances, deep learning methods cannot be easily applied to real-world applications due to the requirement…
Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology,…
In contrast to electronic computation, chemical computation is noisy and susceptible to a variety of sources of error, which has prevented the construction of robust complex systems. To be effective, chemical algorithms must be designed…
We study the set of output stable configurations of chemical reaction deciders (CRDs). It turns out that CRDs with only bimolecular reactions (which are almost equivalent to population protocols) have a special structure that allows for an…
For the investigation of chemical reaction networks, the identification of all relevant intermediates and elementary reactions is mandatory. Many algorithmic approaches exist that perform explorations efficiently and automatedly. These…
The search for pathways that optimize the formation of a particular target molecule in a reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well represented as…
Identifying unique characteristics in a network through comparison with another network is an essential network analysis task. For example, with networks of protein interactions obtained from normal and cancer tissues, we can discover…
Chemical algorithms are statistical algorithms described and represented as chemical reaction networks. They are particularly attractive for traffic shaping and general control of network dynamics; they are analytically tractable, they…
While the field of first-principles explorations into chemical reaction space has been continuously growing, the development of strategies for analyzing resulting chemical reaction networks (CRNs) is lagging behind. A CRN consists of…
A chemical reaction mechanism (CRM) is a sequence of molecular-level events involving bond-breaking/forming processes, generating transient intermediates along the reaction pathway as reactants transform into products. Understanding such…
In recent years, deep learning has made remarkable strides, surpassing human capabilities in tasks like strategy games, and it has found applications in complex domains, including protein folding. In the realm of quantum chemistry, machine…
This paper is concerned with the dynamical properties of deterministically modeled chemical reaction systems with mass-action kinetics. Such models are ubiquitously found in chemistry, population biology, and the burgeoning field of systems…
A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an…
Compared to classical deep neural networks its binarized versions can be useful for applications on resource-limited devices due to their reduction in memory consumption and computational demands. In this work we study deep neural networks…
The large-scale properties of chemical reaction systems, such as the metabolism, can be studied with graph-based methods. To do this, one needs to reduce the information -- lists of chemical reactions -- available in databases. Even for the…