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Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
Networks are a powerful abstraction with applicability to a variety of scientific fields. Models explaining their morphology and growth processes permit a wide range of phenomena to be more systematically analysed and understood. At the…
The fundamental decomposition of a chemical reaction network (CRN) is induced by partitioning the reaction set into "fundamental classes". It was the basis of the Higher Deficiency Algorithm for mass action systems of Ji and Feinberg, and…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…
Many important phenomena in biochemistry and biology exploit dynamical features such as multi-stability, oscillations, and chaos. Construction of novel chemical systems with such rich dynamics is a challenging problem central to the fields…
Biological networks provide insight into the complex organization of biological processes in a cell at the system level. They are an effective tool for understanding the comprehensive map of functional interactions, finding the functional…
Empirical data on real complex systems are becoming increasingly available. Parallel to this is the need for new methods of reconstructing (inferring) the topology of networks from time-resolved observations of their node-dynamics. The…
Across many disciplines, chemical reaction networks (CRNs) are an established population model defined as a system of coupled nonlinear ordinary differential equations. In many applications, for example, in systems biology and epidemiology,…
Random graph models have been instrumental in characterizing complex networks, but chemical reaction networks (CRNs) are better represented as hypergraphs. Traditional models of random CRNs often reduce CRNs to bipartite graphs,…
Can we employ one neural model to efficiently dismantle many complex yet unique networks? This article provides an affirmative answer. Diverse real-world systems can be abstracted as complex networks each consisting of many functional nodes…
The aim of this work is to make available to the community a large collection of mass-action reaction networks of a given size for further research. The set is limited to what can be computed on a modern multi-core desktop in reasonable…
A dynamical system obtains a wide variety of kinetic realizations, which is advantageous for the analysis of biochemical systems. A reaction network, derived from a dynamical system, may or may not possess some properties needed for a…
Understanding propagation mechanisms in complex networks is essential for fields like epidemiology and multi-robot networks. This paper reviews various propagation models, from traditional deterministic frameworks to advanced data-driven…
Filters in a Convolutional Neural Network (CNN) contain model parameters learned from enormous amounts of data. In this paper, we suggest to decompose convolutional filters in CNN as a truncated expansion with pre-fixed bases, namely the…
The transition in random fiber networks from two-dimensional to three-dimensional planar structure driven by increasing coverage (total fiber length per unit area) is studied with a deposition model. At low coverage the network geometry…
The development of chemical reaction models aids understanding and prediction in areas ranging from biology to electrochemistry and combustion. A systematic approach to building reaction network models uses observational data not only to…
This paper is concerned with the utilization of deterministically modeled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary…
Multimode fibers (MMFs) have the potential to carry complex images for endoscopy and related applications, but decoding the complex speckle patterns produced by mode-mixing and modal dispersion in MMFs is a serious challenge. Several groups…
Understanding biological network dynamics is a fundamental issue in various scientific and engineering fields. Network theory is capable of revealing the relationship between elements and their propagation; however, for complex collective…
Biological data including gene expression data are generally high-dimensional and require efficient, generalizable, and scalable machine-learning methods to discover their complex nonlinear patterns. The recent advances in machine learning…