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A novel method for correcting the effect of nonlinear distortion in orthogonal frequency division multiplexing signals is proposed. The method depends on adaptively selecting the distortion over a subset of the data carriers, and then using…
The problem of effectively combining data with a mathematical model constitutes a major challenge in applied mathematics. It is particular challenging for high-dimensional dynamical systems where data is received sequentially in time and…
In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…
Nonlinearity of power amplifier is one of the major limitations to the achievable capacity in wireless transmission systems. Nonlinear impairments are determined by the nonlinear distortions of the power amplifier and modulator…
We consider the problem of minimizing a sum of several convex non-smooth functions. We introduce a new algorithm called the selective linearization method, which iteratively linearizes all but one of the functions and employs simple…
Transmission line, or wire, is always troublesome to integrated circuits designers, but it could be helpful to parallel computing researchers. This paper proposes the Virtual Transmission Method (VTM), which is a new distributed and…
We propose a method for adaptive nonlinear sequential modeling of vector-time series data. Data is modeled as a nonlinear function of past values corrupted by noise, and the underlying non-linear function is assumed to be approximately…
In this report, we develop a semistability analysis framework for nonlinear systems with bounded time-varying delays with applications to stability analysis of multiagent dynamic networks with consensus protocols in the presence of unknown…
Nonlinearity continuation method, applied to boundary value problems for steady-state Richards equation, gradually approaches the solution through a series of intermediate problems. Originally, the Newton method with simple line search…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
This work develops a nonlinear multigrid method for diffusion problems discretized by cell-centered finite volume methods on general unstructured grids. The multigrid hierarchy is constructed algebraically using aggregation of degrees of…
Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…
Power distribution systems are increasingly exposed to large voltage fluctuations driven by intermittent renewable generation and time varying loads (e.g., electric vehicles and storage). To address this challenge, a number of advanced…
The paper deals with a non-linear system largely used in biology, which, in certain conditions and for particular coefficient values, becomes linear, with a linear diagram over a large range of time. It can be used as a veritable regulator…
Telecommunication networks make extensive use of power amplifiers to broaden the coverage from transmitter to receiver. Achieving high power efficiency is challenging and comes at a price: the wanted linear performance is degraded due to…
In this article we consider the iterative solution of the linear system of equations arising from the discretisation of the poly-energetic linear Boltzmann transport equation using a discontinuous Galerkin finite element approximation in…
The Duffing oscillator is a paradigm of bistable oscillatory motion in physics, engineering, and biology. Time series of such oscillations are often observed experimentally in a nonlinear system excited by a spontaneously fluctuating force.…
Numerous audio systems for musicians are expensive and bulky. Therefore, it could be advantageous to model them and to replace them by computer emulation. In guitar players' world, audio systems could have a desirable nonlinear behavior…
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…
In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…