Related papers: Basis-Independent Spectral Methods for Non-linear …
We study in this paper the problem of adaptive trajectory tracking for nonlinear systems affine in the control with bounded state-dependent and time-dependent uncertainties. We propose to use a modular approach, in the sense that we first…
In this note we address the problem of indirect adaptive (regulation or tracking) control of nonlinear, input affine dissipative systems. It is assumed that the supply rate, the storage and the internal dissipation functions may be…
An electromagnetic response of a single graphene layer to a uniform, arbitrarily strong electric field $E(t)$ is calculated by solving the kinetic Boltzmann equation within the relaxation-time approximation. The theory is valid at low…
We establish a novel approach to probing spatially resolved multi-time correlation functions of interacting many-body systems, with scalable experimental overhead. Specifically, designing nonlinear measurement protocols for multidimensional…
This paper discusses the solution of nonlinear integral equations with noisy integral kernels as they appear in nonparametric instrumental regression. We propose a regularized Newton-type iteration and establish convergence and convergence…
The structure of the electronic nonlinear optical conductivity is elucidated in a detailed study of the time-reversal symmetric two-band model. The nonlinear conductivity is decomposed as a sum of contributions related with different…
Graphical models have long been studied in statistics as a tool for inferring conditional independence relationships among a large set of random variables. The most existing works in graphical modeling focus on the cases that the data are…
We study the influence of different kinds of gaps in a quasiparticle spectrum on longitudinal and transverse optical conductivities of bilayer graphene. An exact analytical expression for magneto-optical conductivity is derived using a…
Nonlinear light-matter interactions are typically enhanced by increasing the local field and its interaction time with matter. Conventional methods to achieve these goals are based on resonances or slow-light effects. However, these methods…
A key assumption in the theory of nonlinear adaptive control is that the uncertainty of the system can be expressed in the linear span of a set of known basis functions. While this assumption leads to efficient algorithms, it limits…
We present a comprehensive analysis of the the nonlinear optical Kerr effect in graphene. We directly solve the S-matrix element to calculate the absorption rate, utilizing the Volkov-Keldysh- type crystal wave functions. We then convert to…
We propose a flexible method for estimating luminosity functions (LFs) based on kernel density estimation (KDE), the most popular nonparametric density estimation approach developed in modern statistics, to overcome issues surrounding…
We study the problem of passive imaging through convolutive channels. A scene is illuminated with an unknown, unstructured source, and the measured response is the convolution of this source with multiple channel responses, each of which is…
This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear…
We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…
We propose an advanced Chebyshev expansion method for the numerical calculation of linear response functions at finite temperature. Its high stability and the small required resources allow for a comprehensive study of the optical…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic…
We report on the observation of the nonlinear intensity dependence of the bulk photogalvanic current and photoconductivity in the twisted graphene with small twist angles close to the second magical angle. We show that terahertz radiation…
A theoretical approach for a non-perturbative dynamical description of two interacting atoms in an optical lattice potential is introduced. The approach builds upon the stationary eigenstates found by a procedure described in Grishkevich et…