Related papers: Homeostasis and injectivity: a reaction network pe…
Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from…
[Background] Several studies have mentioned network modularity -- that a network can easily be decomposed into subgraphs that are densely connected within and weakly connected between each other -- as a factor affecting metabolic…
In this note, we use a result by Harris (1957) to show that there always exists a stationary measure (not necessarily a distribution) on a closed irreducible component of a stochastic reaction network. This measure might not be unique. In…
Most classical (non-spiking) neural network models disregard internal neuron dynamics and treat neurons as simple input integrators. However, biological neurons have an internal state governed by complex dynamics that plays a crucial role…
Genetic regulatory networks are defined by their topology and by a multitude of continuously adjustable parameters. Here we present a class of simple models within which the relative importance of topology vs. interaction strengths becomes…
In view of ever-changing conditions both in the external world and in intrinsic brain states, maintaining the robustness of computations poses a challenge, adequate solutions to which we are only beginning to understand. At the level of…
A detailed understanding of biochemical networks at the molecular level is essential for studying complex cellular processes. In this paper, we provide a comprehensive description of biochemical networks by considering individual atoms and…
A natural condition on the structure of the underlying chemical reaction network, namely weak reversibility, is shown to guarantee the existence of an equilibrium (steady state) in each positive stoichiometric compatibility class for the…
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,…
The behavior of the network and its stability are governed by both dynamics of individual nodes as well as their topological interconnections. Attention mechanism as an integral part of neural network models was initially designed for…
The brain is believed to operate in part by making predictions about sensory stimuli and encoding deviations from these predictions in the activity of "prediction error neurons." This principle defines the widely influential theory of…
The sensitivities revealed by a sensitivity analysis of a probabilistic network typically depend on the entered evidence. For a real-life network therefore, the analysis is performed a number of times, with different evidence. Although…
Dynamical system models of complex biochemical reaction networks are usually high-dimensional, nonlinear, and contain many unknown parameters. In some cases the reaction network structure dictates that positive equilibria must be unique for…
Chemical reaction networks describe interactions between biochemical species. Once an underlying reaction network is given for a biochemical system, the system dynamics can be modelled with various mathematical frameworks such as continuous…
In this study, we explore the inherent trade-off between accuracy and robustness in neural networks, drawing an analogy to the uncertainty principle in quantum mechanics. We propose that neural networks are subject to an uncertainty…
Reaction networks can display a wide array of dynamics. However, it is possible for different reaction networks to display the same dynamics. This phenomenon is called dynamical equivalence and makes network identification a hard problem to…
The goal of polyhomeostatic control is to achieve a certain target distribution of behaviors, in contrast to polyhomeostatic regulation which aims at stabilizing a steady-state dynamical state. We consider polyhomeostasis for individual and…
In this paper we study the local instability to the boundary equilibria and the local stability to the positive equilibria for some chemical reaction-diffusion systems. We first analyze a three-species system with boundary equilibria in…
Zero-one biochemical reaction networks play key roles in cell signalling such as signalling pathways regulated by protein phosphorylation. Multistability of reaction networks is a crucial dynamics feature enabling decision-making in cells.…
Reaction-diffusion systems driven far from thermodynamic equilibrium through the injection of energy can support multiple distinct spatial patterns that persist as long-lived dynamical phases. The stability of these metastable phases is not…