Related papers: Differential Renormalization and Dimensional Reduc…
We present an overview of the Density Matrix Renormalization Group and its connections to Quantum Groups, Matrix Products and Conformal Field Theory. We emphasize some common formal structures in all these theories. We also propose…
How to obtain the desirable representation of a 3D shape is a key challenge in 3D shape retrieval task. Most existing 3D shape retrieval methods focus on capturing shape representation with different neural network architectures, while the…
We calculate O(alpha_s) two-loop virtual corrections to the differential decay width dGamma(B --> X_s l^+ l^-)/ds, where s is the invariant mass squared of the lepton pair. We also include those contributions from gluon bremsstrahlung which…
We compute the one-loop renormalization of the Planck mass for type II string theories compactified to four dimensions on symmetric orbifolds that preserve ${\cal N}=2$ supersymmetry. Depending on the orbifold, the effect can be as large as…
An analytical renormalization group treatment is presented of a model which, for one value of parameters, is equivalent to diffusion limited aggregation. The fractal dimension of DLA is computed to be 2-1/2+1/5=1.7. Higher multifractal…
A general model of dialton-Maxwell gravity in two dimensions is investigated. The corresponding one-loop effective action and the generalized $\beta$-functions are obtained. A set of models that are fixed points of the renormalization group…
Overparametrized neural networks trained by gradient descent (GD) can provably overfit any training data. However, the generalization guarantee may not hold for noisy data. From a nonparametric perspective, this paper studies how well…
The problem of reconstructing a two-dimensional (2D) current distribution in a superconductor from a 2D magnetic field measurement is recognized as a first-kind integral equation and resolved using the method of Regularization.…
I comment and summarize the principles underlying the Four Dimensional Regularization/Renormalization (FDR) approach to the UV and IR infinities. A few recent results are also reviewed.
Quantum gravitational effects on the renormalization group equation are studied in the $(2+\epsilon)$-dimensional approach. Divergences in a matter one-loop effective action do not receive gravitational radiative corrections. The…
This paper proposes a generalized framework with joint normalization which learns lower-dimensional subspaces with maximum discriminative power by making use of the Riemannian geometry. In particular, we model the similarity/dissimilarity…
The curvature on codimension-two and higher branes is not regular for arbitrary matter sources. Nevertheless, the low-energy theory for an observer on such a brane should be well-defined and independent to any regularization procedure. This…
L2 regularization for weights in neural networks is widely used as a standard training trick. However, L2 regularization for gamma, a trainable parameter of batch normalization, remains an undiscussed mystery and is applied in different…
We introduce a new massive renormalization scheme, denoted mSMOM, as a modification of the existing RI/SMOM scheme. We use SMOM for defining renormalized fermion bilinears in QCD at non-vanishing fermion mass. This scheme has properties…
Dimensionality reduction is a popular preprocessing and a widely used tool in data mining. Transparency, which is usually achieved by means of explanations, is nowadays a widely accepted and crucial requirement of machine learning based…
We suggest a non-minimal renormalization scheme based on dimensional regularization that naturally incorporates threshold effects of heavy particles. By renormalizing couplings and masses to subtract all poles in $d \geq 4$, the resulting…
There are some points to notice in the dimensional reduction of the off-shell supergravity. We discuss a consistent way of the dimensional reduction of five-dimensional off-shell supergravity compactified on S^1/Z_2. There are two…
We give a simple and elegant proof of the Equivalence Theorem, stating that two field theories related by nonlinear field transformations have the same S matrix. We are thus able to identify a subclass of nonrenormalizable field theories…
We study one loop corrections to $N=\frac{1}{2}$ supersymmetric $SU(N)\times U(1)$ pure gauge theory. We calculate divergent contributions of the 1PI graphs contain the non-anti-commutative parameter $C$ up to one loop corrections. We find…
The free (4,0) superconformal theory in 6 dimensions and its toroidal dimensional reductions are studied. The reduction to four dimensions on a 2-torus has an $SL(2,\Z)$ duality symmetry that acts non-trivially on the linearised gravity…