Related papers: Boolean analysis of lateral inhibition
We study synchronisation properties of networks of coupled dynamical systems with interaction akin to diffusion. We assume that the isolated node dynamics possesses a forward invariant set on which it has a bounded Jacobian, then we…
We overview networks which characterise dynamics in cellular automata. These networks are derived from one-dimensional cellular automaton rules and global states of the automaton evolution: de Bruijn diagrams, subsystem diagrams, basins of…
As a discrete approach to genetic regulatory networks, Boolean models provide an essential qualitative description of the structure of interactions among genes and proteins. Boolean models generally assume only two possible states…
In the recently developed theory of isospectral transformations of networks isospectral compressions are performed with respect to some chosen characteristic (attribute) of nodes (or edges) of networks. Each isospectral compression (when a…
In this work we consider random Boolean networks that provide a general model for genetic regulatory networks. We extend the analysis of James Lynch who was able to proof Kauffman's conjecture that in the ordered phase of random networks,…
Boolean networks can be viewed as functions on the set of binary strings of a given length, described via logical rules. They were introduced as dynamic models into biology, in particular as logical models of intracellular regulatory…
It is a common belief that the order of a Boolean network is mainly determined by its attractors, including fixed points and cycles. Using semi-tensor product (STP) of matrices and the algebraic state-space representation (ASSR) of Boolean…
Boolean threshold networks have recently been proposed as useful tools to model the dynamics of genetic regulatory networks, and have been successfully applied to describe the cell cycles of \textit{S. cerevisiae} and \textit{S. pombe}.…
There is a wealth of applied problems that can be posed as a dynamical system defined on a network with both attractive and repulsive interactions. Some examples include: understanding synchronization properties of nonlinear oscillator;,…
A broad range of nonlinear processes over networks are governed by threshold dynamics. So far, existing mathematical theory characterizing the behavior of such systems has largely been concerned with the case where the thresholds are…
The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them.…
This paper considers a nonlinear dynamical system on a complex, finite dimensional Banach space which has an asymptotically stable, hyperbolic fixed point. We investigate the connection between the so-called principle eigenfunctions of the…
This article investigates a family of centrality models for urban networks that incorporate both topological and non-topological factors. Since centrality is inherently recursive, these models can be formulated as fixed-point equations,…
In this paper, we study geometric properties of basins of attraction of monotone systems. Our results are based on a combination of monotone systems theory and spectral operator theory. We exploit the framework of the Koopman operator,…
Network inference has been extensively studied in several fields, such as systems biology and social sciences. Learning network topology and internal dynamics is essential to understand mechanisms of complex systems. In particular, sparse…
We investigate the dynamics of continuous attractor neural networks (CANNs). Due to the translational invariance of their neuronal interactions, CANNs can hold a continuous family of stationary states. We systematically explore how their…
Sequences of neural activity arise in many brain areas, including cortex, hippocampus, and central pattern generator circuits that underlie rhythmic behaviors like locomotion. While network architectures supporting sequence generation vary…
We develop a novel analytical method for studying optimal paths in dynamic optimization problems under general monotonicity conditions. The method centers on a locator function -- a simple object constructed directly from the model's…
One of the characteristic features of genetic networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random errors. In this paper, we seek to better understand how robustness is…
Complexity in the temporal organization of neural systems may be a reflection of the diversity of its neural constituents. These constituents, excitatory and inhibitory neurons, comprise an invariant ratio in vivo and form the substrate for…