Related papers: Basis-Independent Spectral Methods for Non-linear …

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a…

The problem of calculation of the reflectivity of non-ideal shock-compressed plasmas is revisited. The dielectric formalism based on the method of moments incorporating exact asymptotic forms and sum rules is applied to the new experimental…

Model inference for dynamical systems aims to estimate the future behaviour of a system from observations. Purely model-free statistical methods, such as Artificial Neural Networks, tend to perform poorly for such tasks. They are therefore…

Employing the Kernel Polynomial method (KPM), we study the electronic properties of the graphene bilayers in the presence of diagonal disorder, within the tight-binding approximation. The KPM method enables us to calculate local density of…

Modern Bayesian optimization and adaptive sampling methods increasingly rely on nonlinear parametric models, yet theoretical guarantees for such models under adaptive data collection remain limited. Existing analyses largely focus on…

A methodology for non-intrusive, projection-based non-linear model reduction originally presented by Renganathan et. al. (2018)~\cite{renganathan2018koopman} is further extended towards parametric systems with focus on application to…

Topological insulators (TI) are highly attractive platforms for next-generation optoelectronic and photonic devices. Spin-momentum locking of topological surface states enhance their nonlinear optical responses and sensitivities, especially…

Calculation of the coherent nonlinear response of a system is essential to correctly interpret results from advanced techniques such as two-dimensional coherent spectroscopy (2DCS). Usually, even for the simplest systems, such calculations…

This paper proposes a novel formulation of frequency response for nonlinear systems in the Koopman operator framework. This framework is a promising direction for the analysis and synthesis of systems with nonlinear dynamics based on…

Biased bilayer graphene, with its easily tunable band gap, presents itself as the ideal system to explore the excitonic effect in graphene based systems. In this paper we study the excitonic optical response of such a system by combining a…

Although massless Dirac fermions in graphene constitute a centrosymmetric medium for in-plane excitations, their second-order nonlinear optical response is nonzero if the effects of spatial dispersion are taken into account. Here we present…

We present a fermionic description of non-equilibrium multi-level systems. Our approach uses the Keldysh path integral formalism and allows us to take into account periodic drives, as well as dissipative channels. The technique is based on…

Multiple solutions are common in various non-convex problems arising from industrial and scientific computing. Nonetheless, understanding the nontrivial solutions' qualitative properties seems limited, partially due to the lack of efficient…

Interpretation of time-resolved spectroscopies such as transient absorption (TA) or two-dimensional (2D) spectroscopy often relies on the perturbative description of light-matter interaction. In many cases the third order of nonlinear…

In this paper we present computational techniques to investigate the solutions of two-component, nonlinear reaction-diffusion (RD) systems on arbitrary surfaces. We build on standard techniques for linear and nonlinear analysis of RD…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

We investigate optical transitions of non-interacting electron systems consisting of two symmetric energy bands touching each other at the Fermi energy (e.g. graphene at half filling). Optical conductivity is obtained using Kubo formula at…

We address the optical conductivity of undoped bilayer graphene in the presence of a finite bias voltage at finite temperature. The effects of gap parameter and stacking type on optical conductivity are discussed in the context of tight…

In this study we systematically measure the near-infrared spectral dependence, the sub-picosecond temporal evolution and pulse-width dependence of the effective Kerr coefficient ($n_{2,eff}$) of graphene in hundreds of femtosecond regime.…