Related papers: Higher-order perturbation theory for highly-improv…
In this paper, two classes of continuous higher order adaptive sliding mode controllers based on barrier functions are developed for a perturbed chain of integrators with unbounded perturbations. Both classes provide finite-time convergence…
We give an introduction to three topics in lattice gauge theory: I. The Schroedinger Functional and O(a) improvement. O(a) improvement has been reviewed several times. Here we focus on explaining the basic ideas in detail and then proceed…
We give an introduction to the special problems encountered in a treatment of HQET beyond perturbation theory in the gauge coupling constant. In particular, we report on a recent test of HQET as an effective theory for QCD and discuss how…
Nonperturbative lattice methods are applied to the investigation of strong, electroweak, and gravitational interactions. Selected models of new physics (expected at the TeV scale) are discussed.
Linear control theory is used to develop an improved localized control scheme for spatially extended chaotic systems, which is applied to a Coupled Map Lattice as an example. The optimal arrangement of the control sites is shown to depend…
In this contribution I discuss a recent proposal of a novel action for lattice gauge theory for finite systems, which accommodates non-periodic spatial boundary conditions. Drawing on the summation-by-parts formulation of finite differences…
Based on standard field-theoretic considerations, we develop an effective action approach for investigating quantum phase transitions in lattice Bose systems at arbitrary temperature. We begin by adding to the Hamiltonian of interest a…
Despite growing interest in synchronization dynamics over "higher-order" network models, optimization theory for such systems is limited. Here, we study a family of Kuramoto models inspired by algebraic topology in which oscillators are…
We discuss how lattice calculations can be a useful tool for the study of structure functions. Particular emphasis is given to the perturbative renormalization of the operators.
Networks are a fundamental tool for understanding and modeling complex systems in physics, biology, neuroscience, engineering, and social science. Many networks are known to exhibit rich, lower-order connectivity patterns that can be…
The paper proposes a novel regularization procedure for machine learning. The proposed high-order regularization (HR) provides new insight into regularization, which is widely used to train a neural network that can be utilized to…
We are able to derive the equations of motion for forced mechanical systems in a purely variational setting, both in the context of Lagrangian or Hamiltonian mechanics, by duplicating the variables of the system as introduced by Galley…
The derivation of the Feynman rules for lattice perturbation theory from actions and operators is complicated, especially for highly improved actions such as HISQ. This task is, however, both important and particularly suitable for…
The method of higher covariant derivative regularization of gauge theories is reviewed. The objections raised in the literature last years are discussed and the consistency of the method is proven. New approach to regularization of…
A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather…
We calculate Wilson loops of various sizes up to loop order $n=20$ for lattice sizes of $L^4 (L=4, 6, 8, 12)$ using the technique of Numerical Stochastic Perturbation Theory in quenched QCD. This allows to investigate the behaviour of the…
The perturbative theory of the nucleation kinetics is analyzed. A new improvement is suggested and compared with numerical calculations.
Infrared divergences in the perturbative expansion of gauge theory amplitudes and cross sections have been a focus of theoretical investigations for almost a century. New insights still continue to emerge, as higher perturbative orders are…
We analyze the moments of the isosinglet generalized parton distributions H, E, H-tilde, E-tilde of the nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the…
We compare, for the static potential and at short distances, perturbation theory with the results of lattice simulations. We show that a renormalon-dominance picture explains why in the literature sometimes agreement, and another…