Related papers: Node Balanced Steady States: Unifying and Generali…
For the networks that are linear conjugate to complex balanced systems, the delayed version may include two classes of networks: one class is still linear conjugate to the delayed complex balanced network, the other is not. In this paper,…
The steady-state degree of a chemical reaction network is the number of complex steady-states for generic rate constants and initial conditions. One way to bound the steady-state degree is through the mixed volume of the steady-state system…
For the reaction networks with one-dimensional stoichiometric subspaces, we show the following results. (1) If the maximum number of positive steady states is an even number N, then the maximum number of stable positive steady states is…
We propose a general classification of nonequilibrium steady states in terms of their stationary probability distribution and the associated probability currents. The stationary probabilities can be represented graph-theoretically as…
Controlling complex reaction networks is a fundamental challenge in the fields of physics, biology, and systems engineering. Here, we prove a general principle for catalytic reaction systems with kinetics where the reaction order and the…
Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from…
Social network extensions of Heider's balance theory have not always been consistent. Structural balance theory primarily focuses on graph partitioning, thereby assuming, homogeneity in balance-driven behavior of nodes. We present a general…
One approach to studying the system-wide organization of biochemistry is to use statistical graph theory. Even in such a heavily simplified method, which disregards most of the dynamic aspects of biochemistry, one is faced with fundamental…
Biochemical models that exhibit bistability are of interest to biologists and mathematicians alike. Chemical reaction network theory can provide sufficient conditions for the existence of bistability, and on the other hand can rule out the…
We introduce thermodynamic networks, a general framework for autonomous, physics-based computation using non-equilibrium steady states. These networks are modeled as a collection of finite-size reservoirs that exchange conserved…
Motivation: A Chemical Reaction Network (CRN) is a set of chemical reactions, which can be very complex and difficult to analyze. Indeed, dynamical properties of CRNs can be described by a set of non-linear differential equations that…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
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…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
Using random walk sampling methods for feature learning on networks, we develop a method for generating low-dimensional node embeddings for directed graphs and identifying transition states of stochastic chemical reacting systems. We…
Class imbalance is pervasive in real-world graph datasets, where the majority of annotated nodes belong to a small set of classes (majority classes), leaving many other classes (minority classes) with only a handful of labeled nodes. Graph…
In this paper, the Turing instability in reaction-diffusion models defined on complex networks is studied. Here, we focus on three types of models which generate complex networks, i.e. the Erd\H{o}s-R\'enyi, the Watts-Strogatz, and the…
We study properties of Graph Convolutional Networks (GCNs) by analyzing their behavior on standard models of random graphs, where nodes are represented by random latent variables and edges are drawn according to a similarity kernel. This…
Node classification is an important task to solve in graph-based learning. Even though a lot of work has been done in this field, imbalance is neglected. Real-world data is not perfect, and is imbalanced in representations most of the…
We introduce a mapping between graphs and pure quantum bipartite states and show that the associated entanglement entropy conveys non-trivial information about the structure of the graph. Our primary goal is to investigate the family of…