Related papers: Higher order non-linear parameters with PLANCK
Lin and Zhaos theorem on loop formulas states that in the propositional case the stable model semantics of a logic program can be completely characterized by propositional loop formulas, but this result does not fully carry over to the…
Non-linear renewal theory is extended to include random walks perturbed by both a slowly changing sequence and a stationary one. Main results include a version of the Key Renewal Theorem, a derivation of the limiting distribution of the…
The choice of a suitable regularization parameter is an important part of most regularization methods for inverse problems. In the absence of reliable estimates of the noise level, heuristic parameter choice rules can be used to accomplish…
In this paper, we will discuss how operational limitations affect input-output behaviours of the system. In particular, we will provide formulations for passivity and passivity indices of a nonlinear system given operational limitations on…
The nonlinear saturation of the tearing mode is revisited in slab geometry by taking into account higher-order harmonics in the outer solution. The general formalism for tackling this problem in the case of a vanishing current gradient at…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
The duality relation between one-loop integrals and phase-space integrals, developed in a previous work, is extended to higher-order loops. The duality relation is realized by a modification of the customary +i0 prescription of the Feynman…
In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable…
An underlying fundamental assumption in relativistic perturbation theory is the existence of a parametric family of spacetimes that can be Taylor expanded around a background. Since the choice of the latter is crucial, sometimes it is…
Recent research on temporal networks has highlighted the limitations of a static network perspective for our understanding of complex systems with dynamic topologies. In particular, recent works have shown that i) the specific order in…
In this paper, we show a series of abstract results on fixed point regularity with respect to a parameter. They are based on a Taylor development taking into account a loss of regularity phenomenon, typically occurring for composition…
Maximum likelihood method is widely used for parameter estimation in high energy physics. To consider various systematic uncertainties, tens of or even hundreds of nuisance parameters (NP) are introduced in a likelihood fit. The constraint…
Amplitude expansions are used to determine steady states of a semi-infinite solid subject to the Grinfeld instability in systems with a fixed (wave)length. We present two methods to obtain high-order weakly nonlinear results. Using the…
We consider correlation functions containing the axial current of one light and one heavy quark in the static approximation as well as in full QCD, using the lattice regularization. Up to one-loop order of perturbation theory, we study the…
We establish and develop a novel methodology to treat higher-order non-linear effects of gravitational radiation that is scattered from binary inspirals, which employs modern scattering-amplitudes methods on the effective picture of the…
Kernel-based approach to operator approximation for partial differential equations has been shown to be unconditionally stable for linear PDEs and numerically exhibit unconditional stability for non-linear PDEs. These methods have the same…
The main goal of this paper is the study of two kinds of nonlinear problems depending on parameters in unbounded domains. Using a nonstandard variational approach, we first prove the existence of bounded solutions for nonlinear eigenvalue…
The ability to generate multiple plans is central to using planning in real-life applications. Top-quality planners generate sets of such top-cost plans, allowing flexibility in determining equivalent ones. In terms of the order between…
One of the most severe limitations in particle accelerators and beam transport are non-linear effects. Techniques to study and possibly suppress some of these detrimental effects exist, the most popular are based on particle tracking and…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…