Related papers: Selection, Stability and Renormalization
For singular perturbation problems in dynamical systems, various appropriate singular perturbation methods have been proposed to eliminate secular terms appearing in the naive expansion. For example, the method of multiple time scales, the…
We consider a stabilized finite element method based on a spacetime formulation, where the equations are solved on a global (unstructured) spacetime mesh. A unique continuation problem for the wave equation is considered, where data is…
Complex networks have acquired a great popularity in recent years, since the graph representation of many natural, social and technological systems is often very helpful to characterize and model their phenomenology. Additionally, the…
We first introduce the percolation problems associated with the graph theoretical concepts of $(k,l)$-sparsity, and make contact with the physical concepts of ordinary and rigidity percolation. We then devise a renormalization…
For scalar QED on a three-dimensional toroidal lattice with a fine lattice spacing we consider the renormalization problem of choosing counter terms depending on the lattice spacing, so that the theory stays finite as the spacing goes to…
A perturbative description of Large Scale Structure is a cornerstone of our understanding of the observed distribution of matter in the universe. Renormalization is an essential and defining step to make this description physical and…
Power transforms are popular parametric methods for making data more Gaussian-like, and are widely used as preprocessing steps in statistical analysis and machine learning. However, we find that direct implementations of power transforms…
We propose prioritized unit propagation with periodic resetting, which is a simple but surprisingly effective algorithm for solving random SAT instances that are meant to be hard. In particular, an evaluation on the Random Track of the 2017…
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 discuss recently developed methods that quantify the stability and generalizability of statistical findings under distributional changes. In many practical problems, the data is not drawn i.i.d. from the target population. For example,…
We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy…
For certain hierarchical structures, one can study the percolation problem using the renormalization-group method in a very precise way. We show that the idea can be also applied to two-dimensional planar lattices by regarding them as…
The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes…
First, we consider the problem of hedging in complete binomial models. Using the discrete-time F\"ollmer-Schweizer decomposition, we demonstrate the equivalence of the backward induction and sequential regression approaches. Second, in…
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 $O(N)$…
We consider the systematic force on a heavy probe induced by interaction with an overdamped diffusive medium where particles undergo a rotating force around a fixed center. The stiffness matrix summarizes the stability of the probe around…
We discuss the perturbative expansion of several one-loop improved renormalisation group equations. It is shown that in general the integrated renormalisation group flows fail to reproduce perturbation theory beyond one loop.
In this paper we introduce the randomised stability constant for abstract inverse problems, as a generalisation of the randomised observability constant, which was studied in the context of observability inequalities for the linear wave…
We consider energy norm a posteriori error analysis of conforming finite element approximations of singularly perturbed reaction-diffusion problems on simplicial meshes in arbitrary space dimension. Using an equilibrated flux…
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…