相关论文: Renormgroup symmetry for solution functionals

A method of ``blocking'' triangulations that rests on the self-similarity feature of dynamically triangulated random manifolds is proposed. The method is used to define the renormalization group for random geometries. As an illustration,…

Symbolic integration deals with the evaluation of integrals in closed form. We present an overview of Risch's algorithm including recent developments. The algorithms discussed are suited for both indefinite and definite integration. They…

The renormalization group (RG) is a powerful theoretical framework developed to consistently transform the description of configurations of systems with many degrees of freedom, along with the associated model parameters and coupling…

This is a brief overview of our work on the theory of group invariant solutions to differential equations. The motivations and applications of this work stem from problems in differential geometry and relativistic field theory. The key…

It is argued that universality is severely limited for models with multiple fixed points. As a demonstration the renormalization group equations are presented for the potential and the wave function renormalization constants in the $O(N)$…

The functional renormalisation group is employed to study the non-linear regime of late-time cosmic structure formation. This framework naturally allows for non-perturbative approximation schemes, usually guided by underlying symmetries or…

In this paper we consider the problem of quantizing theories defined over configuration spaces described by non-commuting parameters. If one tries to do that by generalizing the path-integral formalism, the first problem one has to deal…

We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss the anharmonic oscillator and the single impurity Anderson model. We…

In this work we introduce a formulation for a non-local Hessian that combines the ideas of higher-order and non-local regularization for image restoration, extending the idea of non-local gradients to higher-order derivatives. By carefully…

Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less…

A renormalization group method with the Lie symmetry is presented for the singular perturbation problems. Asymptotic solutions are obtained as group-invariant solutions under approximate Lie group admitted by perturbed differential…

This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…

If supersymmetric particles are discovered, an important problem will be to determine how supersymmetry has been broken. At collider energies, supersymmetry breaking can be parameterised by soft supersymmetry breaking parameters. Several…

The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…

We discuss issues of problem formulation for algorithms in real algebraic geometry, focussing on quantifier elimination by cylindrical algebraic decomposition. We recall how the variable ordering used can have a profound effect on both…

We explore the possibilities of using the fermionic functional renormalization group to compute the phase diagram of systems with competing instabilities. In order to overcome the ubiquituous divergences encountered in RG flows, we propose…

An algorithm of the tensor renormalization group is proposed based on a randomized algorithm for singular value decomposition. Our algorithm is applicable to a broad range of two-dimensional classical models. In the case of a square…

In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a…

Promising resolutions of the generalization puzzle observe that the actual number of parameters in a deep network is much smaller than naive estimates suggest. The renormalization group is a compelling example of a problem which has very…

The Generalized Method of Moments (GMM) is a partition of unity based technique for solving electromagnetic and acoustic boundary integral equations. Past work on the GMM for electromagnetics was confined to geometries modeled by piecewise…