Related papers: Lessons from Numerical Analysis
The model of two-level Kondo effect is studied by the Wilson numerical renormalization group method. It is shown that there exist a new type of weak-coupling fixed point other than the strong-coupling fixed point found by Vladar and…
We study the three-dimensional $SU(2)$ principal chiral model (PCM) using different tensor renormalization group methods based on the triad and anisotropic decomposition of the tensor. The tensor network representation is formulated based…
We study clustering methods for binary data, first defining aggregation criteria that measure the compactness of clusters. Five new and original methods are introduced, using neighborhoods and population behavior combinatorial optimization…
Concise variable transformations between the four angles of the CKM matrix in the standard representation advocated by the Particle Data Group and the angles of the unitarity triangles are derived. The behavior of these transformations in…
Some renormalization group approaches have been proposed during the last few years which are close in spirit to the Nightingale phenomenological procedure. In essence, by exploiting the finite size scaling hypothesis, the approximate…
The vNRQCD Lagrangian for colored heavy scalar fields in the fundamental representation of QCD and the renormalization group analysis of the corresponding operators are presented. The results are an important ingredient for renormalization…
We present two different approaches for parameter learning in several mixture models in one dimension. Our first approach uses complex-analytic methods and applies to Gaussian mixtures with shared variance, binomial mixtures with shared…
A Monte Carlo Renormalization Group algorithm is used on the Ising model to derive critical exponents and the critical temperature. The algorithm is based on a minimum relative entropy iteration developed previously to derive potentials…
We review the method of differential renormalization, paying special attention to a new constrained version for symmetric theories.
Clustering is widely used in different field such as biology, psychology, and economics. Most traditional clustering algorithms are limited to handling datasets that contain either numeric or categorical attributes. However, datasets with…
This paper studies countable systems of linearly and hierarchically interacting diffusions taking values in the positive quadrant. These systems arise in population dynamics for two types of individuals migrating between and interacting…
We report a real-space renormalization group (RSRG) algorithm, which is formulated through Baxter's corner transfer matrix (CTM), for two-dimensional (d = 2) classical lattice models. The new method performs the renormalization group…
We investigate Hamiltonian systems with two degrees of freedom by using renormalization group method. We show that the original Hamiltonian systems and the renormalization group equations are integrable if the renormalization group…
We investigate an operator renormalization group method to extract and describe the relevant degrees of freedom in the evolution of partial differential equations. The proposed renormalization group approach is formulated as an analytical…
I outline why the renormalisation group is needed to analyse the scale dependence and hence determine the power counting for effective theories of strongly interacting systems. I summarise the results of several such analyses for two- and…
Based on the Renormalization Group method, a reduction of non integrable multi-dimensional hamiltonian systems has been performed. The evolution equations for the slowly varying part of the angle-averaged phase space density, and for the…
The algebraic method of renormalization is applied to the standard model of electroweak interactions. We present the most important modifications compared to theories with simple groups.
The locations of multicritical points on many hierarchical lattices are numerically investigated by the renormalization group analysis. The results are compared with an analytical conjecture derived by using the duality, the gauge symmetry…
Divergence-form operators with random coefficients homogenize over large scales. Over the last decade, an intensive research effort focused on turning this asymptotic statement into quantitative estimates. The goal of this note is to review…
I explain the methods that are used in field theory for problems involving typical momenta on two or more widely disparate scales. The principal topics are: (a) renormalization, which treats the problem of taking an ultra-violet cut-off to…