Related papers: Non-normality, optimality and synchronization
An interfacial approximation of the streamer stage in the evolution of sparks and lightning can be written as a Laplacian growth model regularized by a `kinetic undercooling' boundary condition. We study the linear stability of uniformly…
This paper studies the data-driven control of unknown linear-threshold network dynamics to stabilize the state to a reference value. We consider two types of controllers: (i) a state feedback controller with feed-forward reference input and…
Sparse random networks contain structures that can be considered as diluted feed-forward networks. Modeling of cortical circuits has shown that feed-forward structures, if strongly pronounced compared to the embedding random network, enable…
The loss surface of deep neural networks has recently attracted interest in the optimization and machine learning communities as a prime example of high-dimensional non-convex problem. Some insights were recently gained using spin glass…
A widely believed explanation for the remarkable generalization capacities of overparameterized neural networks is that the optimization algorithms used for training induce an implicit bias towards benign solutions. To grasp this…
There has been much recent progress in forecasting the next observation of a linear dynamical system (LDS), which is known as the improper learning, as well as in the estimation of its system matrices, which is known as the proper learning…
We consider synchronization of coupled dynamical systems when different types of interactions are simultaneously present. We assume that a set of dynamical systems are coupled through the connections of two or more distinct networks (each…
This brief paper further investigates the locally and globally adaptive synchronization of an uncertain complex dynamical network. Several network synchronization criteria are deduced. Especially, our hypotheses and designed adaptive…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
Control of complex processes is a major goal of network analyses. Most approaches to control nonlinearly coupled systems require the network topology and/or network dynamics. Unfortunately, neither the full set of participating nodes nor…
Consistency regularization-based methods are prevalent in semi-supervised learning (SSL) algorithms due to their exceptional performance. However, they mainly depend on domain-specific data augmentations, which are not usable in domains…
The stable functionality of networked systems is a hallmark of their natural ability to coordinate between their multiple interacting components. Yet, strikingly, real-world networks seem random and highly irregular, apparently lacking any…
We consider a one-dimensional directional array of diffusively coupled oscillators. They are perturbed by the injection of a small additive noise, typically orders of magnitude smaller than the oscillation amplitude, and the system is…
We introduce a new family of algorithms for detecting and estimating a rank-one signal from a noisy observation under prior information about that signal's direction, focusing on examples where the signal is known to have entries biased to…
We study with numerical simulation the possible limit behaviors of synchronous discrete-time deterministic recurrent neural networks composed of N binary neurons as a function of a network's level of dilution and asymmetry. The network…
Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to…
Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this…
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…
In recent years, new regularization methods based on (deep) neural networks have shown very promising empirical performance for the numerical solution of ill-posed problems, e.g., in medical imaging and imaging science. Due to the…
The inevitable random frequency differences among semiconductor lasers present an obstacle to achieving their collective coherence, but previous worked showed that fully (all-to-all) coupled networks can still be synchronized even in the…