Related papers: Analysis of Boolean Functions based on Interaction…
The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy…
We analyze the quantum entanglement properties of bosonic particles hopping over graph structures.Mode-entanglement of a graph vertex with respect the rest of the graph is generated, starting from a product state, by turning on for a finite…
A conjunctive Boolean network (CBN) is a finite state dynamical system, whose variables take values from a binary set, and the value update rule for each variable is a Boolean function consisting only of logic AND operations. We investigate…
Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes to enable integrative multiscale simulations. Whereas traditional models focus on the structure…
Graphs have been utilized as a powerful tool to model pairwise relationships between people or objects. Such structure is a special type of a broader concept referred to as hypergraph, in which each hyperedge may consist of an arbitrary…
Boolean networks have been successfully used in modelling gene regulatory networks. In this paper we propose a reduction method that reduces the complexity of a Boolean network but keeps dynamical properties and topological features and…
Homogeneous Boltzmann-type equations are an established tool for modelling interacting multi-agent systems in sociophysics by means of the principles of statistical mechanics and kinetic theory. A customary implicit assumption is that…
We introduce a taxonomy of interaction types and show that graphs are focal hypergraphs: every graph is canonically a focal hypergraph via its closed neighbourhood structure, and every graph dynamical model is a special case of the general…
Graph rewrite formalisms are a powerful approach to modeling complex molecular systems. They capture the intrinsic concurrency of molecular interactions, thereby enabling a formal notion of mechanism (a partially ordered set of events) that…
We develop a general method to explore how the function performed by a biological network can constrain both its structural and dynamical network properties. This approach is orthogonal to prior studies which examine the functional…
Feature interaction is crucial in predictive machine learning models, as it captures the relationships between features that influence model performance. In this work, we focus on pairwise interactions and investigate their importance in…
Sequences of correlated binary patterns can represent many time-series data including text, movies, and biological signals. These patterns may be described by weighted combinations of a few dominant structures that underpin specific…
Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea applied to graphs. In order to understand expressive power and…
Empirical evidence has revealed that biological regulatory systems are controlled by high-level coordination between topology and Boolean rules. In this study, we study the joint effects of degree and Boolean functions on the stability of…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
We demonstrate the effects of embedding subgraphs using a Boolean network, which is one of the discrete dynamical models for transcriptional regulatory networks. After comparing the dynamical properties of network embedded seven different…
We analyse the problem of solving Boolean equation systems through the use of structure graphs. The latter are obtained through an elegant set of Plotkin-style deduction rules. Our main contribution is that we show that equation systems…
We study the challenges of applying deep learning to gene expression data. We find experimentally that there exists non-linear signal in the data, however is it not discovered automatically given the noise and low numbers of samples used in…
Random Boolean networks have been used widely to explore aspects of gene regulatory networks. A modified form of the model through which to systematically explore the effects of increasing the number of gene states has previously been…
Advances in deep learning models have revolutionized the study of biomolecule systems and their mechanisms. Graph representation learning, in particular, is important for accurately capturing the geometric information of biomolecules at…