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Directed acyclic graphs are a fundamental class of networks that includes citation networks, food webs, and family trees, among others. Here we define a random graph model for directed acyclic graphs and give solutions for a number of the…

The Jacobian matrix of a dynamic system and its principal minors play a prominent role in the study of qualitative dynamics and bifurcation analysis. When interpreting the Jacobian as an adjacency matrix of an interaction graph, its…

Analysis of chemical graphs is a major research topic in computational molecular biology due to its potential applications to drug design. One approach is inverse quantitative structure activity/property relationship (inverse QSAR/QSPR)…

In recent years, there have been intense research efforts to develop efficient methods for probabilistic inference in probabilistic influence diagrams or belief networks. Many people have concluded that the best methods are those based on…

In clinical treatment, identifying potential adverse reactions of drugs can help assist doctors in making medication decisions. In response to the problems in previous studies that features are high-dimensional and sparse, independent…

We extend the merging model for undirected networks by Kim et al. [Eur. Phys. J. B 43, 369 (2004)] to directed networks and investigate the emerging scale-free networks. Two versions of the directed merging model, friendly and hostile…

Graph rewrite systems are powerful tools to model and study complex problems in various fields of research. Their successful application to chemical reaction modelling on a molecular level was shown but no appropriate and simple system is…

Zipper logic is a graph rewrite system, consisting in only local rewrites on a class of zipper graphs. Connections with the chemlambda artificial chemistry and with knot diagrammatics based computation are explored in the article.

The discovery of peptides having high biological activity is very challenging mainly because there is an enormous diversity of compounds and only a minority have the desired properties. To lower cost and reduce the time to obtain promising…

In this paper it is shown that it is possible to associate several polynomial ideals to a directed graph $D$ in order to find properties of it. In fact by using algebraic tools it is possible to give appropriate procedures for automatic…

Digital twins, used to represent physical systems, have been lauded as tools for understanding reality. Complex system behavior is typically captured in domain-specific models crafted by subject experts. Contemporary methods for employing…

Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active…

Artificial intelligence (AI) has undergone a renaissance recently, making major progress in key domains such as vision, language, control, and decision-making. This has been due, in part, to cheap data and cheap compute resources, which…

Estimating the health impacts of exposure to a mixture of chemicals poses many statistical challenges: multiple correlated exposure variables, moderate to high dimensionality, and possible nonlinear and interactive health effects of mixture…

Online social networks are a dominant medium in everyday life to stay in contact with friends and to share information. In Twitter, users can connect with other users by following them, who in turn can follow back. In recent years,…

Predicting whether a chemical structure shares a desired biological effect can have a significant impact for in-silico compound screening in early drug discovery. In this study, we developed a deep learning model where compound structures…

We describe a large class of chemical reaction networks, those endowed with a subtle structural property called concordance. We show that the class of concordant networks coincides precisely with the class of networks which, when taken with…

At the intersection of computation and cognitive science, graph theory is utilized as a formalized description of complex relationships and structures. Traditional graph models are often static, lacking dynamic and autonomous behavioral…

The goal of this paper is to gather and develop some necessary and sufficient criteria for injectivity and multistationarity in vector fields associated with a chemical reaction network under a variety of more or less general assumptions on…

We study the problem of constructing synthetic graphs that resemble real-world directed graphs in terms of their degree correlations. We define the problem of directed 2K construction (D2K) that takes as input the directed degree sequence…