Related papers: Exclusion Sensitivity of Boolean Functions
Recently it was conjectured that nodal domains of random wave functions are adequately described by critical percolation theory. In this paper we strengthen this conjecture in two respects. First, we show that, though wave function…
We consider the interplay between nonlocal nonlinearity and randomness for two different nonlinear Schr\"odinger models. We show that stability of bright solitons in presence of random perturbations increases dramatically with the…
We introduce a theoretical framework for understanding and predicting the complexity of sequence classification tasks, using a novel extension of the theory of Boolean function sensitivity. The sensitivity of a function, given a…
Observing finite regions of a bigger system is a common experience, from microscopy to molecular simulations. In the latter especially, there is ongoing interest in predicting thermodynamic properties from tracking fluctuations in finite…
We give the first agnostic, efficient, proper learning algorithm for monotone Boolean functions. Given $2^{\tilde{O}(\sqrt{n}/\varepsilon)}$ uniformly random examples of an unknown function $f:\{\pm 1\}^n \rightarrow \{\pm 1\}$, our…
We study models of correlated percolation where there are constraints on the occupation of sites that mimic force-balance, i.e. for a site to be stable requires occupied neighboring sites in all four compass directions in two dimensions. We…
Percolation in an information-theoretically secure graph is considered where both the legitimate and the eavesdropper nodes are distributed as Poisson point processes. For both the path-loss and the path-loss plus fading model, upper and…
We study the noise properties of ballistic conductors with carriers satisfying fractional exclusion statistics. To test directly the nature of exclusion statistics we found that systems under weakly degenerate conditions should be…
Following the Flory ideality hypothesis intrachain and interchain excluded volume interactions are supposed to compensate each other in dense polymer systems. Multi-chain effects should thus be neglected and polymer conformations may be…
A randomly interacting N-species Lotka-Volterra system in the presence of a Gaussian multiplicative noise is analyzed. The investigation is focused on the role of this external noise into the statistical properties of the extinction times…
We prove that nested canalizing functions are the minimum-sensitivity Boolean functions for any given activity ratio and we characterize the sensitivity boundary which has a nontrivial fractal structure. We further observe, on an extensive…
Robust loss functions are essential for training deep neural networks with better generalization power in the presence of noisy labels. Symmetric loss functions are confirmed to be robust to label noise. However, the symmetric condition is…
We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…
The transfer matrix and matrix multiplication ansatz, when applied to nonequilibrium steady states in asymmetric exclusion processed and traffic models, has given many exact results for phase diagrams, bulk densities and fluxes, as well as…
We consider the effect of noise in sparse Boolean Networks with redundant functions. We show that they always exhibit a non-zero error level, and the dynamics undergoes a phase transition from non-ergodicity to ergodicity, as a function of…
While classical percolation is well understood, percolation effects in randomly packed or jammed structures are much less explored. Here we investigate both experimentally and theoretically the electrical percolation in a binary composite…
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous and discrete time-filters for stochastic dynamic systems with non-linear state dynamics and linear measurements under…
The notion of neural collapse refers to several emergent phenomena that have been empirically observed across various canonical classification problems. During the terminal phase of training a deep neural network, the feature embedding of…
Recent research on the dynamics of certain fluid dynamical instabilities shows that when there is a slow invariant manifold subject to fast timescale instability the dynamics are extremely sensitive to noise. The behaviour of such systems…
We extend the statistical neurodynamics to study transient dynamics of sequence processing neural networks with finite dilution, and the theoretical results is supported by the extensive numerical simulations. It is found that the order…