相关论文: Dimensional Reduction applied to QCD at higher ord…
We investigate the so-called ``Kaluza-Klein regularisation'' procedure in supersymmetric extensions of the standard model with additional compact dimensions and Scherk-Schwarz mechanism for supersymmetry breaking. This procedure uses a…
Coordinate descent algorithms solve optimization problems by successively performing approximate minimization along coordinate directions or coordinate hyperplanes. They have been used in applications for many years, and their popularity…
Dimensionality reduction (DR) is a popular method for preparing and analyzing high-dimensional data. Reduced data representations are less computationally intensive and easier to manage and visualize, while retaining a significant…
A dimension reduction for the hyperbolic space is established. When points are far apart an embedding with bounded distortion into the hyperbolic plane is achieved.
A many variable $q$-calculus is introduced using the formalism of braided covector algebras. Its properties when certain of its deformation parameters are roots of unity are discussed in detail, and related to fractional supersymmetry. The…
Contributions to the decay rates of P-wave charmonium states that are proportional to $n_f \alpha_s^3$, where $n_f$ is the number of flavors of light quarks, are calculated in the framework of nonrelativistic QCD using the threshold…
We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and,…
Most past work on weak nonleptonic decays has mixed dimensional regularization in the weak operator product expansion with some form of a cutoff regularization in the evaluation of the matrix elements. Even with the usual technique of…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
Based on a more careful canonical analysis, we motivate a reduced quantization - in the sense of superspace quantization - of slightly inhomogeneous cosmology in place of the Dirac quantization in the existing literature, and provide it in…
One of the much-debated novel features of theories with extra dimensions is the presence of power-like loop corrections to gauge coupling unification, which have the potential of allowing a significant reduction of the unification scale. A…
A 3D-2D dimension reduction for $-\Delta_1$ is obtained. A power law approximation from $-\Delta_p$ as $p \to 1$ in terms of $\Gamma$- convergence, duality and asymptotics for least gradient functions has also been provided.
We study the corrections to $\epsilon^\prime /\epsilon$ in the minimal supersymmetric model at the leading order in QCD and QED. Supersymmetry can increase the standard model prediction for $\epsilon^\prime /\epsilon$ by at most 40\% for…
In 1998 the Adapted Ordering Method was developed for the study of the representation theory of the superconformal algebras in two dimensions. It allows: to determine the maximal dimension for a given type of space of singular vectors, to…
A recently proposed renormalization group approach to dimensional crossover in quasi-one-dimensional quantum antiferromagnets is improved and then shown to give identical results, in some cases, to those obtained earlier.
The H\"older continuity of the truncated moment map of a shade function in Euclidean space is established in the vicinity of a principal semi-algebraic set. The proof combines volume bounds of semi-algebraic sets and convex optimization…
Proper regularization is critical for speeding up training, improving generalization performance, and learning compact models that are cost efficient. We propose and analyze regularized gradient descent algorithms for learning shallow…
Supersymmetry is studied in 2+1 dimensions. In addition to the multiplets corresponding to those in 3+1 dimensions the Clifford algebra allows an extra set. When the extra chiral multiplet is included, formulating supersymmetric QED3 in the…
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through a subtle approximation of the shape Hessian,…
Within the framework of QCD we compute renormalization constants for the strong coupling and the quark masses to four-loop order. We apply the DR-bar scheme and put special emphasis on the additional couplings which have to be taken into…