Related papers: Cooperative Boolean systems with generically long …
AND-OR networks are Boolean networks where each coordinate function is either the AND or OR logical operator. We study the number of fixed points of these Boolean networks in the case that they have a wiring diagram with chain topology. We…
The controllability and observability of Boolean control network(BCN) are two fundamental properties. But the verification of latter is much harder than the former. This paper considers the observability of BCN via controllability. First,…
A natural measure of smoothness of a Boolean function is its sensitivity (the largest number of Hamming neighbors of a point which differ from it in function value). The structure of smooth or equivalently low-sensitivity functions is still…
In this paper, we propose an approach for modeling and analysis of a number of phenomena of collective behavior. By collectives we mean multi-agent systems that transition from one state to another at discrete moments of time. The behavior…
Many real-world networks can be modeled by networks of interacting agents. Analysis of these interactions can reveal fundamental properties from these networks. Estimating the amount of collaboration in a network corresponding to…
We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only…
Dynamic Bayesian networks have been well explored in the literature as discrete-time models: however, their continuous-time extensions have seen comparatively little attention. In this paper, we propose the first constraint-based algorithm…
We investigate the dynamical and spectral consequences of capacitance-network-mediated interactions in superconducting transmon arrays beyond effective nearest-neighbor descriptions. While weak coupling regimes are well captured by an…
We study a class of self-adjoint operators defined on the direct sum of two Hilbert spaces: a finite dimensional one called sometimes a ``small subsystem'' and an infinite dimensional one -- a ``reservoir''. The operator, which we call 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,…
We leverage proof techniques Fourier analysis and an existing result in coding theory to derive new bounds for the problem of non-interactive simulation of binary random variables. Previous bounds in the literature were derived by applying…
Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions (from molecules in gene regulatory…
We prove that, to compute a Boolean function $f$ on $N$ variables with error probability $\epsilon$, any quantum black-box algorithm has to query at least $\frac{1 - 2\sqrt{\epsilon}}{2} \rho_f N = \frac{1 - 2\sqrt{\epsilon}}{2} \bar{S}_f$…
Boolean networks have been used in a variety of settings, as models for general complex systems as well as models of specific systems in diverse fields, such as biology, engineering, and computer science. Traditionally, their properties as…
Cooperative behavior constitutes a key aspect of human society and non-human animal systems, but explaining how cooperation evolves represents a major scientific challenge. It is now well established that social network structure plays a…
A new analytical framework consisting of two phenomena: single sample and multiple samples, is proposed to deal with the identification problem of Boolean control networks (BCNs) systematically and comprehensively. Under this framework, the…
Computational models of biological processes provide one of the most powerful methods for a detailed analysis of the mechanisms that drive the behavior of complex systems. Logic-based modeling has enhanced our understanding and…
We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete…
In this paper, we consider the cooperative output regulation problem for heterogeneous linear multi-agent systems in the presence of communication constraints. Under standard assumptions on the agents dynamics, we propose a distributed…
Deep learning models, such as wide neural networks, can be conceptualized as nonlinear dynamical physical systems characterized by a multitude of interacting degrees of freedom. Such systems in the infinite limit, tend to exhibit simplified…