Related papers: Tolerance and Sensitivity in the Fuse Network

We study the instabilities of a harmonic oscillator subject to additive and dichotomous multiplicative noise, focussing on the dependance of the instability threshold on the mass. For multiplicative noise in the damping, the instability…

A bifurcating system subject to multiplicative noise can display on-off intermittency. Using a canonical example, we investigate the extreme sensitivity of the intermittent behavior to the nature of the noise. Through a perturbative…

We consider the influence of local noise on a generalized network of populations having positive and negative feedbacks. The population dynamics at the nodes is nonlinear, typically chaotic, and allows cessation of activity if the…

This work considers the robustness of uncertain consensus networks. The first set of results studies the stability properties of consensus networks with negative edge weights. We show that if either the negative weight edges form a cut in…

The paper studies average consensus with random topologies (intermittent links) \emph{and} noisy channels. Consensus with noise in the network links leads to the bias-variance dilemma--running consensus for long reduces the bias of the…

We study the diversity of complex spatio-temporal patterns of random synchronous asymmetric neural networks (RSANNs). Specifically, we investigate the impact of noisy thresholds on network performance and find that there is a narrow and…

We study the problem of communicating a distributed correlated memoryless source over a memoryless network, from source nodes to destination nodes, under quadratic distortion constraints. We establish the following two complementary…

The rigidity of elastic networks depends sensitively on their internal connectivity and the nature of the interactions between constituents. Particles interacting via central forces undergo a zero-temperature rigidity-percolation transition…

We study the effects of nonzero time delays in stochastic synchronization problems with linear couplings in an arbitrary network. Using the known exact threshold value from the theory of differential equations with delays, we provide the…

Flow and Diffusion Distributed Structures (FDS) are stationary spatially periodic patterns that can be observed in reaction-diffusion-advection systems. These structures arise when the flow rate exceeds a certain bifurcation point provided…

The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two…

Consider an information source generating a symbol at the root of a tree network whose links correspond to noisy communication channels, and broadcasting it through the network. We study the problem of reconstructing the transmitted symbol…

Machine learning classifiers have been demonstrated, both empirically and theoretically, to be robust to label noise under certain conditions -- notably the typical assumption is that label noise is independent of the features given the…

Convolutional Neural Network (CNN) recognition rates drop in the presence of noise. We demonstrate a novel method of counteracting this drop in recognition rate by adjusting the biases of the neurons in the convolutional layers according to…

Transformers achieve state-of-the-art accuracy and robustness across many tasks, but an understanding of their inductive biases and how those biases differ from other neural network architectures remains elusive. In this work, we identify…

Effect of weak disorder on tunneling through a potential barrier is studied analytically. A diagrammatic approach based on the specific behavior of subbarrier wave functions is developed. The problem is shown to be equivalent to that of…

Many real networks present a bounded scale-free behavior with a connectivity cut-off due to physical constraints or a finite network size. We study epidemic dynamics in bounded scale-free networks with soft and hard connectivity cut-offs.…

We investigate the propagation of perturbations in Boolean networks by evaluating the Derrida plot and modifications of it. We show that even small Random Boolean Networks agree well with the predictions of the annealed approximation, but…

Noise in seismic data arises from numerous sources and is continually evolving. The use of supervised deep learning procedures for denoising of seismic datasets often results in poor performance: this is due to the lack of noise-free field…

Research on the vulnerability of electric networks with a complex network approach has produced significant results in the last decade, especially for transmission networks. These studies have shown that there are causal relations between…