Related papers: Stabilizing and Destabilizing Effects of Embedding…
How the architecture of gene regulatory networks ultimately shapes gene expression patterns is an open question, which has been approached from a multitude of angles. The dominant strategy has been to identify non-random features in these…
Recent studies have been using graph theoretical approaches to model complex networks (such as social, infrastructural or biological networks), and how their hardwired circuitry relates to their dynamic evolution in time. Understanding how…
Boolean networks have been used successfully in modeling biological networks and provide a good framework for theoretical analysis. However, the analysis of large networks is not trivial. In order to simplify the analysis of such networks,…
This short paper presents an abstract, tunable model of genomic structural change within the cell lifecycle and explores its use with simulated evolution. A well-known Boolean model of genetic regulatory networks is extended to include…
Networks with nodes embedded in a metric space have gained increasing interest in recent years. The effects of spatial embedding on the networks' structural characteristics, however, are rarely taken into account when studying their…
The low-dimensional manifold hypothesis posits that the data found in many applications, such as those involving natural images, lie (approximately) on low-dimensional manifolds embedded in a high-dimensional Euclidean space. In this…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
In this paper we study the dynamical behavior of Boolean networks with firing memory, namely Boolean networks whose vertices are updated synchronously depending on their proper Boolean local transition functions so that each vertex remains…
Many material response functions depend strongly on microstructure, such as inhomogeneities in phase or orientation. Homogenization presents the task of predicting the mean response of a sample of the microstructure to external loading for…
We consider the problem of embedding a dynamic network, to obtain time-evolving vector representations of each node, which can then be used to describe changes in behaviour of individual nodes, communities, or the entire graph. Given this…
Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…
Many knowledge graph embedding methods operate on triples and are therefore implicitly limited by a very local view of the entire knowledge graph. We present a new framework MOHONE to effectively model higher order network effects in…
Graph neural networks (GNNs) have significantly improved the representation power for graph-structured data. Despite of the recent success of GNNs, the graph convolution in most GNNs have two limitations. Since the graph convolution is…
We analyse a model of fixed in-degree Random Boolean Networks in which the fraction of input-receiving nodes is controlled by a parameter gamma. We investigate analytically and numerically the dynamics of graphs under a parallel XOR…
In automata networks, it is well known that the way entities update their states over time has a major impact on their dynamics. In particular, depending on the chosen update schedule, the underlying dynamical systems may exhibit more or…
In a graph convolutional network, we assume that the graph $G$ is generated wrt some observation noise. During learning, we make small random perturbations $\Delta{}G$ of the graph and try to improve generalization. Based on quantum…
Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this…
The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them.…
Network embeddings learn to represent nodes as low-dimensional vectors to preserve the proximity between nodes and communities of the network for network analysis. The temporal edges (e.g., relationships, contacts, and emails) in dynamic…
An embedding is a mapping from a set of nodes of a network into a real vector space. Embeddings can have various aims like capturing the underlying graph topology and structure, node-to-node relationship, or other relevant information about…