Related papers: Lessons from Numerical Analysis
We point out some limits of the perturbative renormalization group used in statistical mechanics both at and out of equilibrium. We argue that the non perturbative renormalization group formalism is a promising candidate to overcome some of…
We present a renormalization group (RG) procedure which works naturally on a wide class of interacting one-dimension models based on perturbed (possibly strongly) continuum conformal and integrable models. This procedure integrates Kenneth…
Real bipartite networks combine degree-constrained random mixing with structured, locality-like rules. We introduce a statistical filter that benchmarks node-level bipartite clustering against degree-preserving randomizations to classify…
The real-space renormalisation group method can be applied to the Chalker-Coddington model of the quantum Hall transition to provide a convenient numerical estimation of the localisation critical exponent, $\nu$. Previous such studies found…
The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…
We review the theory of renormalization, including perturbative renormalization, regularized functional integrals, Renormalization Group and rigorous renormalization.
We sharply characterize the performance of different penalization schemes for the problem of selecting the relevant variables in the multi-task setting. Previous work focuses on the regression problem where conditions on the design matrix…
We introduce a picture to analyze the density matrix renormalization group (DMRG) numerical method from a quantum information perspective. This leads us to introduce some modifications for problems with periodic boundary conditions in which…
We review recent developments in tensor network approaches, focusing on renormalization group methods. Since they are free from the negative sign and complex action problems, there is growing interest in their application to lattice field…
A new singular perturbation method based on the Lie symmetry group is presented to a system of difference equations. This method yields consistent derivation of a renormalization group equation which gives an asymptotic solution of the…
This article is a pedagogical introduction to the density matrix renormalization group method and its application in quantum chemistry. It presents the easy-to-understand modern formulation based on matrix product states. It is written in…
The Butcher group is a powerful tool to analyse integration methods for ordinary differential equations, in particular Runge--Kutta methods. Recently, a natural Lie group structure has been constructed for this group. Unfortunately, the…
We continue the study of the renormalization group and decoupling of massive fields in curved space, started in the previous article and analyse the higher derivative sector of the vacuum metric-dependent action of the Standard Model. The…
The in-medium similarity renormalization group (IMSRG) is a popular many-body method used for computations of nuclei. It solves the many-body Schr\"odinger equation through a continuous unitary transformation of the many-body Hamiltonian.…
General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action…
Fundamental machine learning theory shows that different samples contribute unequally both in learning and testing processes. Contemporary studies on DNN imply that such sample difference is rooted on the distribution of intrinsic pattern…
MM (majorization--minimization) algorithms are an increasingly popular tool for solving optimization problems in machine learning and statistical estimation. This article introduces the MM algorithm framework in general and via three…
We study sums of the form $\sum_{k=m}^n a_{nk} b_{km}$, where $a_{nk}$ and $b_{km}$ are binomial coefficients or unsigned Stirling numbers. In a few cases they can be written in closed form. Failing that, the sums still share many common…
We develop a method to obtain the large N renormalization group flows for matrix models of 2 dimensional gravity plus branched polymers. This method gives precise results for the critical points and exponents for one matrix models. We show…
In most real-world scenarios, labeled training datasets are highly class-imbalanced, where deep neural networks suffer from generalizing to a balanced testing criterion. In this paper, we explore a novel yet simple way to alleviate this…