Related papers: A Renormalization Group Procedure for Fiber Bundle…
We develop a renormalization group method to investigate synchronization clusters in a one-dimensional chain of nearest-neighbor coupled phase oscillators. The method is best suited for chains with strong disorder in the intrinsic…
Salmhofer [Commun. Math. Phys. 194, 249 (1998)] has recently developed a new renormalization group method for interacting Fermi systems, where the complete flow from the bare action of a microscopic model to the effective low-energy action,…
This lecture provides an introduction to the renormalisation group as applied to scattering of two nonrelativistic particles. As well as forming a framework for constructing effective theories of few-nucleon systems, these ideas also…
We propose a theoretical formulation of protected edge modes in the language of quantum field theories based on the contemporary understanding of the renormalization group. We use bulk and boundary renormalization arguments which have never…
The renormalization group is used to sum the leading-log (LL) contributions to the effective action for a large constant external gauge field in terms of the one-loop renormalization group (RG) function beta, the next-to-leading-log (NLL)…
We present a simple proof of the all-order exponentiation of soft logarithmic corrections to hard processes in perturbative QCD. Our argument is based on proving that all large logs in the soft limit can be expressed in terms of a single…
In this paper, we study renormalization, that is, the procedure for eliminating singularities, for a special model using both combinatorial techniques in the framework of working with formal series, and using a limit transition in a…
Batch Normalization is an important approach to advancing deep learning since it allows multiple networks to train simultaneously. A problem arises when normalizing along the batch dimension because B.N.'s error increases significantly as…
In this thesis we investigate the Renormalization Group (RG) approach in finite-dimensional glassy systems, whose critical features are still not well-established, or simply unknown. We focus on spin and structural-glass models built on…
We compute the two-loop renormalization group equations for all soft supersymmetry-breaking couplings in a general softly broken N=1 supersymmetric model. We also specialize these results to the Minimal Supersymmetric Standard Model.
The renormalization group method has been adapted to the analysis of the long-time behavior of non-linear partial differential equation and has demonstrated its power in the study of critical phenomena of gravitational collapse. In the…
We have developed a nonperturbative functional renormalization group approach for random field models and related disordered systems for which, due to the existence of many metastable states, conventional perturbation theory often fails.…
For perturbed ordinally differential equations, a procedure of renormalization group method is proposed. To uniquely obtain renormalized solutions for given initial conditions, the procedure assumes that the extra integral constants yielded…
We present an extension of the continuous damage fiber bundle model to describe the gradual degradation of highly heterogeneous materials under an increasing external load. Breaking of a fiber in the model is preceded by a sequence of…
We discuss an environmentally friendly renormalization group approach to analyze phase transitions. We intend to apply this method to the Electroweak Phase Transition. This work is in progress. We present some previously obtained results…
In the modeling of complex biological systems, the use of power-law models (such as S-systems and GMA systems) often provides a remarkable accuracy over several orders of magnitude in concentrations, an unusually broad range not fully…
Batch normalization has been widely used to improve optimization in deep neural networks. While the uncertainty in batch statistics can act as a regularizer, using these dataset statistics specific to the training set impairs generalization…
We propose a renormalization group treatment of stochastically growing networks. As an example, we study percolation on growing scale-free networks in the framework of a real-space renormalization group approach. As a result, we find that…
These introductory notes are about functional renormalization group equations and some of their applications. It is emphasised that the applicability of this method extends well beyond critical systems, it actually provides us a general…
The renormalization group method is applied to the study of homogeneous and flat Friedmann-Robertson-Walker type Universes, filled with a causal bulk viscous cosmological fluid. The starting point of the study is the consideration of the…