Related papers: Exclusion Sensitivity of Boolean Functions
Boson sampling, a computational task believed to be classically hard to simulate, is expected to hold promise for demonstrating quantum computational advantage using near-term quantum devices. However, noise in experimental implementations…
We address the problem of finding optimal strategies for computing Boolean symmetric functions. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a Boolean measurement and we…
Percolation theory has been largely used in the study of structural properties of complex networks such as the robustness, with remarkable results. Nevertheless, a purely topological description is not sufficient for a correct…
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…
Robust stability and stochastic stability have separately seen intense study in control theory for many decades. In this work we establish relations between these properties for discrete-time systems and employ them for robust control…
The two-dimensional backward-facing step flow is a canonical example of noise amplifier flow: global linear stability analysis predicts that it is stable, but perturbations can undergo large amplification in space and time as a result of…
Hypergraphs capture the higher-order interactions in complex systems and always admit a factor graph representation, consisting of a bipartite network of nodes and hyperedges. As hypegraphs are ubiquitous, investigating hypergraph…
We establish new separations between the power of monotone and general (non-monotone) Boolean circuits: - For every $k \geq 1$, there is a monotone function in ${\sf AC^0}$ that requires monotone circuits of depth $\Omega(\log^k n)$. This…
We propose a noise-robust learning framework for the Koopman operator of nonlinear dynamical systems, with guaranteed long-term stability and improved model performance for better model-based predictive control tasks. Unlike some existing…
We present Brownian dynamics simulation results of a flexible linear polymer with excluded-volume interactions under shear flow in the presence of active noise. The active noise strongly affects the polymer's conformational and dynamical…
The dynamical organization in the presence of noise of a Boolean neural network with random connections is analyzed. For low levels of noise, the system reaches a stationary state in which the majority of its elements acquire the same…
The ionic conductivity of mixed alkali glasses exhibits a deep minimum as a function of the relative concentrations of the two alkali ions. To study this behaviour we consider a simple one-dimensional model for asymmetric diffusion of two…
The aim of the present paper is to provide a preliminary investigation of the thermodynamics of particles obeying monotone statistics. To render the potential physical applications realistic, we propose a modified scheme called…
During the past 15 years, several extensions of the concepts noise sensitivity and noise stability, first coined in~\cite{schramm2000}, has been studied. The purpose in this paper is to give definitions of this concepts in the setting of…
Nested canalizing Boolean (NCF) functions play an important role in biological motivated regulative networks and in signal processing, in particular describing stack filters. It has been conjectured that NCFs have a stabilizing effect on…
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…
It is known that, by accounting for the multiboson interferences up to a finite order, the output distribution of noisy Boson Sampling, with distinguishability of bosons serving as noise, can be approximately sampled from in a time…
Quantum noise correlations have been employed in several areas in physics including condensed matter, quantum optics and ultracold atom to reveal non-classical states of the systems. So far, such analysis mostly focused on systems in…
We consider a slow passage through a point of loss of stability. If the passage is sufficiently slow, the dynamics are controlled by additive random disturbances, even if they are extremely small. We derive expressions for the `exit value'…
A key fact in the theory of Boolean functions $f : \{0,1\}^n \to \{0,1\}$ is that they often undergo sharp thresholds. For example: if the function $f : \{0,1\}^n \to \{0,1\}$ is monotone and symmetric under a transitive action with…