Related papers: The Renormalization Scale Setting Problem in QCD […
Commensurate scale relations are perturbative QCD predictions which relate observable to observable at fixed relative scale, such as the "generalized Crewther relation", which connects the Bjorken and Gross-Llewellyn Smith deep inelastic…
In the 1960's, four famous scaling relations were developed which relate the six standard critical exponents describing continuous phase transitions in the thermodynamic limit of statistical physics models. They are well understood at a…
In this lecture I present some of the new developments concerning the use of Pade Approximants (PA's) for resumming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale and scheme dependence as compared…
Sharpness is an almost generic assumption in continuous optimization that bounds the distance from minima by objective function suboptimality. It facilitates the acceleration of first-order methods through restarts. However, sharpness…
This paper provides new error bounds on "consistent" reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a…
There exist renormalisation schemes that explicitly preserve the scale invariance of a theory at the quantum level. Imposing a scale invariant renormalisation breaks renormalisability and induces new non-trivial operators in the theory. In…
An important class of structural models studies the determinants of skill formation and the optimal timing of interventions. In this paper, I provide new identification results for these models and investigate the effects of seemingly…
The constraint of a progressive decrease in residual renormalization scale dependence with increasing loop order is developed as a method for obtaining bounds on unknown higher-order perturbative corrections to renormalization-group…
As applied to quantum theories, the program of renormalization is successful for `renormalizable models' but fails for `nonrenormalizable models'. After some conceptual discussion and analysis, an enhanced program of renormalization is…
Reliable confidence measures of metrics derived from medical imaging reconstruction pipelines would improve the standard of decision-making in many clinical workflows. Conformal Prediction (CP) provides a robust framework for producing…
We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a…
In this study, we propose a novel regularization/renormalization scheme that utilizes an auxiliary Feynman parameterization. This approach is employed to align a specified loop diagram with a designated unit of the form $1=\lambda/\lambda$.…
Given a renormalization scheme of QCD, one can define a mass scale $\Lambda_{\rm QCD}$ in terms of the beta function. Under a change of the renormalization scheme, however, $\Lambda_{\rm QCD}$ changes by a multiplicative constant. We…
We discuss the effects of QCD corrections to the on-shell decay $t \to b W$. We resolve the scale ambiguity using the Brodsky-Lepage-Mackenzie scheme, and find that the appropriate coupling constant is $\alpha_{s}^{ \overline{MS}}…
We analyse approximate solutions to an exact renormalisation group equation with particular emphasis on their dependence on the regularisation scheme, which is kept arbitrary. Physical quantities related to the coarse-grained potential of…
The consideration of predictive uncertainty in medical imaging with deep learning is of utmost importance. We apply estimation of both aleatoric and epistemic uncertainty by variational Bayesian inference with Monte Carlo dropout to…
The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium $\eta_Q$ ($Q$ being $c$ or $b$) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the…
The successful training of deep neural networks requires addressing challenges such as overfitting, numerical instabilities leading to divergence, and increasing variance in the residual stream. A common solution is to apply regularization…
This paper considers the problem of data generation for MPC policy approximation. Learning an approximate MPC policy from expert demonstrations requires a large data set consisting of optimal state-action pairs, sampled across the feasible…
Although well described by mean-field theory in the thermodynamic limit, scaling has long been puzzling for finite systems in high dimensions. This raised questions about the efficacy of the renormalization group and foundational concepts…