相关论文: A Path Integral Approach to Effective Non-Linear M…

With multiple potential mediators on the causal pathway from a treatment to an outcome, we consider the problem of decomposing the effects along multiple possible causal path(s) through each distinct mediator. Under Pearl's path-specific…

A modified perturbation theory in the strength of the nonlinear term is used to solve the Nonlinear Schroedinger Equation with a random potential. It is demonstrated that in some cases it is more efficient than other methods. Moreover we…

We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…

We study a model describing the slow flow of a fluid through a deformable, porous, elastic solid undergoing small deformations. The stress-strain relationship of the solid incorporates nonlinear effects, formulated as a perturbation of the…

We develop an Effective Medium Theory to study the electrical transport properties of disordered graphene. The theory includes non-linear screening and exchange-correlation effects allowing us to consider experimentally relevant strengths…

The nonlinear sigma model (NLSM) epitomises a field-theoretical approach to (interacting) electrons in disordered media. These lectures are aimed at the audience who might have vaguely heard about its existence but know very little of what…

$\delta'$-function perturbations and Neumann boundary conditions are incorporated into the path integral formalism. The starting point is the consideration of the path integral representation for the one dimensional Dirac particle together…

A fundamental manifestation of wave scattering in a disordered medium is the highly complex intensity pattern the waves acquire due to multi-path interference. Here we show that these intensity variations can be entirely suppressed by…

A path-integral formalism is proposed for studying the dynamical evolution in time of patterns in an artificial neural network in the presence of noise. An effective cost function is constructed which determines the unique global minimum of…

In the context of dynamical systems, nonlinearity measures quantify the strength of nonlinearity by means of the distance of their input-output behaviour to a set of linear input-output mappings. In this paper, we establish a framework to…

Nonlinear effects are crucial in order to compute the cosmological matter power spectrum to the accuracy required by future generation surveys. Here, a new approach is presented, in which the power spectrum, the bispectrum and higher order…

One of the main challenges in diffusion-based molecular communication is dealing with the non-linearity of reaction-diffusion chemical equations. While numerical methods can be used to solve these equations, a change in the input signals or…

In this chapter we present a general method of constructing the effective equation which describes the behaviour of small-amplitude solutions for a nonlinear PDE in finite volume, provided that the linear part of the equation is a…

We present a data-driven approach to characterizing nonidentifiability of a model's parameters and illustrate it through dynamic as well as steady kinetic models. By employing Diffusion Maps and their extensions, we discover the minimal…

This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…

We define a deterministic integral with respect to irregular paths as a limit of standard line integrals and completely describe a class of all paths for which this integral exists for functions with H\"older exponent in the range of (0,1].…

The path-specific effect (PSE) is of primary interest in mediation analysis when multiple intermediate variables between treatment and outcome are observed, as it can isolate the specific effect through each mediator, thus mitigating…

Nonlinear extension of the integral part of a standard proportional-integral-derivative (PID) feedback control is proposed for perturbed second-order systems. The approach is model-free and requires solely the Lipschitz boundedness of the…

We present a path integral formalism to compute potentials for nonequilibrium steady states, reached by a multiplicative stochastic dynamics. We develop a weak-noise expansion, which allows the explicit evaluation of the potential in…

We consider a nonparametric regression model with continuous endogenous independent variables when only discrete instruments are available that are independent of the error term. Although this framework is very relevant for applied…