Related papers: Quantum autonomous Boolean networks
Boolean variables are such that they take only values on $ \mathbb{Z}_2 \cong \left\{0, 1 \right\} $. \textit{NK}-Kauffman networks are dynamical deterministic systems of $ N $ Boolean functions that depend only on $ K \leq N $ Boolean…
Boolean networks are a valuable class of discrete dynamical systems models, but they remain fundamentally limited by their inability to capture multi-way interactions in their components. To remedy this limitation, we propose a model of…
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…
A Boolean network is a finite dynamical system, whose variables take values from a binary set. The value update rule for each variable is a Boolean function, depending on a selected subset of variables. Boolean networks have been widely…
We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is…
This paper proposes a new parameter for studying Boolean networks: the independence number. We establish that a Boolean network is $k$-independent if, for any set of $k$ variables and any combination of binary values assigned to them, there…
One way to model telecommunication networks are static Boolean models. However, dynamics such as node mobility have a significant impact on the performance evaluation of such networks. Consider a Boolean model in $\mathbb{R}^d$ and a random…
This paper studies the mathematical properties of collectively canalizing Boolean functions, a class of functions that has arisen from applications in systems biology. Boolean networks are an increasingly popular modeling framework for…
In this report, we present a formal approach that addresses the problem of emergence of phase transitions in stochastic and attractive nonlinear threshold Boolean automata networks. Nonlinear networks considered are informally defined on…
A Boolean network is a finite state discrete time dynamical system. At each step, each variable takes a value from a binary set. The value update rule for each variable is a local function which depends only on a selected subset of…
Methods of modeling cellular regulatory networks as diverse as differential equations and Boolean networks co-exist, however, without any closer correspondence to each other. With the example system of the fission yeast cell cycle control…
For years, we have been building models of gene regulatory networks, where recent advances in molecular biology shed some light on new structural and dynamical properties of such highly complex systems. In this work, we propose a novel…
Boolean network models of molecular regulatory networks have been used successfully in computational systems biology. The Boolean functions that appear in published models tend to have special properties, in particular the property of being…
Quantum networks providing shared entanglement over a mesh of quantum nodes will revolutionize the field of quantum information science by offering novel applications in quantum computation, enhanced precision in networks of sensors and…
This paper reviews a class of generic dissipative dynamical systems called N-K models. In these models, the dynamics of N elements, defined as Boolean variables, develop step by step, clocked by a discrete time variable. Each of the N…
As the inevitable development trend of quantum key distribution, quantum networks have attracted extensive attention, and many prototypes have been deployed over recent years. Existing quantum networks based on optical fibers or quantum…
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…
Boolean networks have been the object of much attention, especially since S. Kauffman proposed them in the 1960's as models for gene regulatory networks. These systems are characterized by being defined on a Boolean state space and by…
Neural networks have emerged as a powerful way to approach many practical problems in quantum physics. In this work, we illustrate the power of deep learning to predict the dynamics of a quantum many-body system, where the training is…
Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give…