Related papers: Complex-linear invariants of biochemical networks
Resilience characterizes a system's ability to retain its original function when perturbations happen. In the past years our attention mainly focused on small-scale resilience, yet our understanding of resilience in large-scale network…
This paper deals with the computation of polytopic invariant sets for polynomial dynamical systems. An invariant set of a dynamical system is a subset of the state space such that if the state of the system belongs to the set at a given…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The…
Chemical reaction networks, or CRNs, are known to stably compute semilinear Boolean-valued predicates and functions, provided that all reactions are irreversible. However, this property does not hold for wet-lab implementations, as all…
Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories,…
A number of machine learning tasks entail a high degree of invariance: the data distribution does not change if we act on the data with a certain group of transformations. For instance, labels of images are invariant under translations of…
The two approaches to analyzing the large strain behavior of rubbery networks are phenomenologically, using strain energy functions drawn from continuum mechanics, and molecular models, which apply statistical mechanics to compute the…
Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological,…
Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most…
Biochemical mechanisms with mass action kinetics are often modeled by systems of polynomial differential equations (DE). Determining directly if the DE system has multiple equilibria (multistationarity) is difficult for realistic systems,…
In this review, we give an introduction to the structural and functional properties of the biological networks. We focus on three major themes: topology of complex biological networks like the metabolic and protein-protein interaction…
The design and synthesis of complex and large mimicked biochemical networks de novo is an unsolved problem in synthetic biology. To address this limitation without resorting to ad hoc computations and experiments, a predictive mathematical…
Multistationary chemical reaction networks are of interest to scientists and mathematicians alike. While some criteria for multistationarity exist, obtaining explicit reaction rates and steady states that exhibit multistationarity for a…
Biomedical sciences are increasingly recognising the relevance of gene co-expression-networks for analysing complex-systems, phenotypes or diseases. When the goal is investigating complex-phenotypes under varying conditions, it comes…
Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…
Deep Neural Networks are, from a physical perspective, graphs whose `links` and `vertices` iteratively process data and solve tasks sub-optimally. We use Complex Network Theory (CNT) to represents Deep Neural Networks (DNNs) as directed…
Can we objectively distinguish chemical systems that are able to process meaningful information from those that are not suitable for information processing? Here, we present a formal method to assess the semantic capacity of a chemical…
Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations, typically described using nonlinear models. Such non-monotonic dynamics are…
Computing topological invariants in two-dimensional quasicrystals and super-moire matter is a remarkable open challenge, due to the absence of translational symmetry and the colossal number of sites inherent to these systems. Here, we…