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Scale invariance profoundly influences the dynamics and structure of complex systems, spanning from critical phenomena to network architecture. Here, we propose a precise definition of scale-invariant networks by leveraging the concept of a…
One of the defining features of living systems is their adaptability to changing environmental conditions. This requires organisms to extract temporal and spatial features of their environment, and use that information to compute the…
In a letter published in Molecular Biology Evolution [10], Chen and Zhang argue that the variation of the mutation rate along the Escherichia coli genome that we recently reported [3] cannot be evolutionarily optimised. To support this…
We show that standard ResNet architectures can be made invertible, allowing the same model to be used for classification, density estimation, and generation. Typically, enforcing invertibility requires partitioning dimensions or restricting…
We propose a new neural network design paradigm Reversible Column Network (RevCol). The main body of RevCol is composed of multiple copies of subnetworks, named columns respectively, between which multi-level reversible connections are…
The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using…
We analyze a model of interacting agents (e.g. prebiotic chemical species) which are represended by nodes of a network, whereas their interactions are mapped onto directed links between these nodes. On a fast time scale, each agent follows…
The exploration of the structural topology and the organizing principles of genome-based large-scale metabolic networks is essential for studying possible relations between structure and functionality of metabolic networks. Topological…
We review recent work on the statistical mechanics of Von Neumann's growth model and discuss its application to cellular metabolic networks. In this context, we present a detailed analysis of the physiological scenario underlying optimality…
The identification of motifs--subgraphs that appear significantly more often in a particular network than in an ensemble of randomized networks--has become a ubiquitous method for uncovering potentially important subunits within networks…
Galled trees are widely studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into galled networks by relaxing a structural condition. In this work, a linear recurrence formula is given…
Gene regulatory networks constitute the first layer of the cellular computation for cell adaptation and surveillance. In these webs, a set of causal relations is built up from thousands of interactions between transcription factors and…
In this paper we present an algorithm to address the predecessor problem of feed-forward Boolean networks. We propose an probabilistic algorithm, which solves this problem in linear time with respect to the number of nodes in the network.…
We live in a world driven by data. The amount of it outgrows anyone's ability to oversee it or even observe its scope. Along with all the advances in the space of data management, there is still a significant lack of formalism and…
Novel method of reconstructing dynamical networks from empirically measured time series is proposed. By examining the variable--derivative correlation of network node pairs, we derive a simple equation that directly yields the adjacency…
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…
For decades, complex networks, such as social networks, biological networks, chemical networks, technological networks, have been used to study the evolution and dynamics of different kinds of complex systems. These complex systems can be…
First we shortly review the different kinds of network modelling methods for systems biology with an emphasis on the different subtypes of logical models, which we review in more detail. Then we show the advantages of Boolean networks…
Many biological networks have been labelled scale-free as their degree distribution can be approximately described by a powerlaw distribution. While the degree distribution does not summarize all aspects of a network it has often been…
Biological systems are driven by intricate interactions among the complex array of molecules that comprise the cell. Many methods have been developed to reconstruct network models of those interactions. These methods often draw on large…