Related papers: The Bussgang Decomposition of Non-Linear Systems: …
Causal discovery in real-world systems, such as biological networks, is often complicated by feedback loops and incomplete data. Standard algorithms, which assume acyclic structures or fully observed data, struggle with these challenges. To…
In this work we formulate a generalized theoretical model to describe the nonlinear dynamics observed in combined frequency-amplitude modulators whose characteristic parameters exhibit a nonlinear dependence on the input modulating signal.…
Cell-free massive MIMO (multiple-input multiple-output) is a key enabler for the sixth generation (6G) of mobile networks, offering significant spectral and energy efficiency gains through user-centric operation of distributed access points…
We study synchronization of nonlinear systems that satisfy an incremental passivity property. We consider the case where the control input is subject to a class of disturbances, including constant and sinusoidal disturbances with unknown…
One of the fundamental steps toward understanding a complex system is identifying variation at the scale of the system's components that is most relevant to behavior on a macroscopic scale. Mutual information provides a natural means of…
We consider the demixing problem of two (or more) structured high-dimensional vectors from a limited number of nonlinear observations where this nonlinearity is due to either a periodic or an aperiodic function. We study certain families of…
In a multiple linear regression model, the algebraic formula of the decomposition theorem explains the relationship between the univariate regression coefficient and partial regression coefficient using geometry. It was found that…
Many natural and manmade dynamical systems that are modeled as large nonlinear multi-oscillator systems like power systems are hard to analyze. For such a system, we propose a nonlinear modal decoupling (NMD) approach inversely constructing…
The problem of linear equivalence for a general class of nonlinear systems, is examined throughout this paper. A relevant algorithm is developed, based on a factorization procedure. This factorization is based on the star-product, an…
It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…
The distortion from massive MIMO (multiple-input--multiple-output) base stations with nonlinear amplifiers is studied and its radiation pattern is derived. The distortion is analyzed both in-band and out-of-band. By using an orthogonal…
Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for…
A linear decomposition of states underpins many classical systems. This is the case of the Helmholtz decomposition, used to split vector fields into divergence-free and potential components, and of the dry Boussinesq system in atmospheric…
Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…
Non-reciprocal systems can be thought of as disobeying Newtons third law - an action does not cause an equal and opposite reaction. In recent years there has been a dramatic rise in interest towards such systems. On a fundamental level,…
Objective: Mixtures of temporally nonstationary signals are very common in biomedical applications. The nonstationarity of the source signals can be used as a discriminative property for signal separation. Herein, a semi-blind source…
Dissipation is a ubiquitous phenomenon in dynamical systems encountered in nature because no finite system is fully isolated from its environment. In optical systems, a key challenge facing any technological application has traditionally…
Theory of nonlinear resonance, including stochastic one, is developed on the basis of the statistical field theory and using variables action-angle. Explicit expressions of action, proper frequency and nonlinearity parameter as functions of…
Koopman analysis provides a general framework from which to analyze a nonlinear dynamical system in terms of a linear operator acting on an infinite-dimensional observable space. This theoretical framework provides a rigorous underpinning…
Nonlinear oscillations are commonly observed in complex systems far from equilibrium, such as living organisms. These oscillations are essential for sustaining vital processes, like neuronal firing, circadian rhythms, and heartbeats. In…