Related papers: Upper bound for the stability of Boolean networks
Bayesian network (BN) structure discovery algorithms typically either make assumptions about the sparsity of the true underlying network, or are limited by computational constraints to networks with a small number of variables. While these…
This paper studies the observability radius of network systems, which measures the robustness of a network to perturbations of the edges. We consider linear networks, where the dynamics are described by a weighted adjacency matrix, and…
We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively…
Dynamical entities interacting with each other on complex networks often exhibit multistability. The stability of a desired steady regime (e.g., a synchronized state) to large perturbations is critical in the operation of many real-world…
Understanding how network function constrains neural connectivity is a central challenge in neuroscience. An influential approach is to train neural networks with gradient descent on cognitive tasks and characterize the resulting…
We derive several upper bounds for the superfluid stiffness $D_s$ for Bose and Fermi systems in terms of expectation values of local operators using linear response theory and variational methods. These give insight into the non-trivial…
Using Boolean networks as prototypical examples, the role of symmetry in the dynamics of heterogeneous complex systems is explored. We show that symmetry of the dynamics, especially in critical states, is a controlling feature that can be…
We study the target control problem of asynchronous Boolean networks, to identify a set of nodes, the perturbation of which can drive the dynamics of the network from any initial state to the desired steady state (or attractor). We are…
We derive an upper bound on the maximum balanced bipartite entanglement entropy of ground states of many-body Hamiltonians defined on a graph, agnostic to any particular model, that possesses a nontrivial automorphism group. We show that…
The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the…
We prove that the fully asynchronous dynamics of a Boolean network $f:\{0,1\}^n\to\{0,1\}^n$ without negative loop can be simulated, in a very specific way, by a monotone Boolean network with $2n$ components. We then use this result to…
We introduce the nested canalyzing depth of a function, which measures the extent to which it retains a nested canalyzing structure. We characterize the structure of functions with a given depth and compute the expected activities and…
We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…
We realize autonomous Boolean networks by using logic gates in their autonomous mode-of-operation on a field-programmable gate array. This allows us to implement time-continuous systems with complex dynamical behaviors that can be…
Our daily social and political life is more and more impacted by social networks. The functioning of our living bodies is deeply dependent on biological regulation networks such as neural, genetic, and protein networks. And the physical…
Athermal models of disordered fibrous networks are highly useful for studying the mechanics of elastic networks composed of stiff biopolymers. The underlying network architecture is a key aspect that can affect the elastic properties of…
Here, we provide an overview of theoretical approaches to semiflexible polymers and their networks. Such semiflexible polymers have large bending rigidities that can compete with the entropic tendency of a chain to crumple up into a random…
Identification of attractors, that is, stable states and sustained oscillations, is an important step in the analysis of Boolean models and exploration of potential variants. We describe an approach to the search for asynchronous cyclic…
When is it safe to approximate a complicated random Boolean network (RBN) as a simplified, easier to model RBN? When can static measures of network structure be reliably used to infer the network's dynamics? This simple experiment tests the…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…