Related papers: Homeostasis in Input-Output Networks: Structure, C…
A mathematical model for a two-gene regulatory network is derived and several of their properties analyzed. Due to the presence of mixed continuous/discrete dynamics and hysteresis, we employ a hybrid systems model to capture the dynamics…
Interconnected ensembles of biological entities are perhaps some of the most complex systems that modern science has encountered so far. In particular, scientists have concentrated on understanding how the complexity of the interacting…
A biological regulatory network can be modeled as a discrete function that contains all available information on network component interactions. From this function we can derive a graph representation of the network structure as well as of…
Soft biological tissues exhibit a tendency to maintain a preferred state of tensile stress, known as tensional homeostasis, which is restored even after external mechanical stimuli. This macroscopic behavior can be described using the…
Molecular networks guide the biochemistry of a living cell on multiple levels: its metabolic and signalling pathways are shaped by the network of interacting proteins, whose production, in turn, is controlled by the genetic regulatory…
This work is concerned with interconnected networks with non-identical subsystems. We investigate the output consensus of the network where the dynamics are subject to external disturbance and/or reference input. For a network of…
Homeostasis of protein concentrations in cells is crucial for their proper functioning, and this requires concentrations (at their steady-state levels) to be stable to fluctuations. Since gene expression is regulated by proteins such as…
We explore the behaviour of chaotic oscillators in hierarchical networks coupled to an external chaotic system whose intrinsic dynamics is dissimilar to the other oscillators in the network. Specifically, each oscillator couples to the…
Symmetry -- invariance to certain operators -- is a fundamental concept in many branches of physics. We propose ways to measure symmetric properties of vertices, and their surroundings, in networks. To be stable to the randomness inherent…
Dynamic networks are structured interconnections of dynamical systems (modules) driven by external excitation and disturbance signals. In order to identify their dynamical properties and/or their topology consistently from measured data, we…
We consider a basic model of a dynamical distribution network, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
Based on extensive study of a dynamical systems model of the development of a cell society, a novel theory for stem cell differentiation and its regulation is proposed as the ``chaos hypothesis''. Two fundamental features of stem cell…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
A set of core features is set forth as the essence of a thermodynamic description, which derive from large-deviation properties in systems with hierarchies of timescales, but which are \emph{not} dependent upon conservation laws or…
Biomolecular networks have already found great utility in characterizing complex biological systems arising from pair-wise interactions amongst biomolecules. Here, we review how graph theoretical approaches can be applied not only for a…
We analyze transport on a graph with multiple constraints and where the weight of the edges connecting the nodes is a dynamical variable. The network dynamics results from the interplay between a nonlinear function of the flow, dissipation,…
The relationship between network topology and system dynamics has significant implications for unifying our understanding of the interplay among metabolic, gene-regulatory, and ecosystem network architecures. Here we analyze the stability…
The control of dynamical, networked systems continues to receive much attention across the engineering and scientific research fields. Of particular interest is the proper way to determine which nodes of the network should receive external…
The relationship between the regulatory design and the functionality of molecular networks is a key issue in biology. Modules and motifs have been associated to various cellular processes, thereby providing anecdotal evidence for…
Power system coherency refers to the phenomenon that machines in a power network exhibit similar frequency responses after disturbances, and is foundational for model reduction and control design. Despite abundant empirical observations,…