Related papers: A Graph Theoretical Approach for Testing Binomiali…

Motivated by problems from Chemical Reaction Network Theory, we investigate whether steady state ideals of reversible reaction networks are generated by binomials. We take an algebraic approach considering, besides concentrations of…

We consider the problem of binomiality of the steady state ideals of biochemical reaction networks. We are interested in finding polynomial conditions on the parameters such that the steady state ideal of a chemical reaction network is…

Analyzing qualitative behaviors of biochemical reactions using its associated network structure has proven useful in diverse branches of biology. As an extension of our previous work, we introduce a graph-based framework to calculate steady…

Binomial ideals are special polynomial ideals with many algorithmically and theoretically nice properties. We discuss the problem of deciding if a given polynomial ideal is binomial. While the methods are general, our main motivation and…

In this paper we discuss the question of how to decide when a general chemical reaction system is incapable of admitting multiple equilibria, regardless of parameter values such as reaction rate constants, and regardless of the type of…

Binary classification problems can be naturally modeled as bipartite graphs, where we attempt to classify right nodes based on their left adjacencies. We consider the case of labeled bipartite graphs in which some labels and edges are not…

We present a novel method for identifying a biochemical reaction network based on multiple sets of estimated reaction rates in the corresponding reaction rate equations arriving from various (possibly different) experiments. The current…

Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…

Biochemical mechanisms with mass action kinetics are often modeled by systems of polynomial differential equations (DE). Determining directly if the DE system has multiple equilibria (multistationarity) is difficult for realistic systems,…

We present a systematic investigation using graph neural networks (GNNs) to model organic chemical reactions. To do so, we prepared a dataset collection of four ubiquitous reactions from the organic chemistry literature. We evaluate seven…

Chemical reaction network theory provides powerful tools for rigorously understanding chemical reactions and the dynamical systems and differential equations that represent them. A frequent issue with mathematical analyses of these networks…

Retrosynthesis is one of the fundamental problems in organic chemistry. The task is to identify reactants that can be used to synthesize a specified product molecule. Recently, computer-aided retrosynthesis is finding renewed interest from…

We consider linear elimination of variables in steady state equations of a chemical reaction network. Particular subsets of variables corresponding to sets of so-called reactant-noninteracting species, are introduced. The steady state…

We extend previous work on injectivity in chemical reaction networks to general interaction networks. Matrix- and graph-theoretic conditions for injectivity of these systems are presented. A particular signed, directed, labelled, bipartite…

We study linear systems of equations with coefficients in a generic partially ordered ring $R$ and a unique solution, and seek conditions for the solution to be nonnegative, that is, every component of the solution is a quotient of two…

This paper studies graph-based active learning, where the goal is to reconstruct a binary signal defined on the nodes of a weighted graph, by sampling it on a small subset of the nodes. A new sampling algorithm is proposed, which…

Recently, techniques for applying convolutional neural networks to graph-structured data have emerged. Graph convolutional neural networks (GCNNs) have been used to address node and graph classification and matrix completion. Although the…

Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…

Graph neural networks are widely used to learn global representations of graphs, which are then used for regression or classification tasks. Typically, the graphs in such data sets are connected, i.e. each training sample consists of a…

We study the data-driven selection of causal graphical models using constraint-based algorithms, which determine the existence or non-existence of edges (causal connections) in a graph based on testing a series of conditional independence…