Related papers: A generalized mean field theory of coarse-graining
We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…
This paper builds on the theory of generalised functions begun in [1]. The Colombeau theory of generalised scalar fields on manifolds is extended to a nonlinear theory of generalised tensor fields which is diffeomorphism invariant and has…
These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does not require either a preferred notion of…
This work is the continuation of the earlier efforts to apply the mean field approximation to the world sheet formulation of planar phi^3 theory. The previous attempts were either simple but without solid foundation or well founded but…
Generative diffusion models can provide powerful prior probability models for inverse problems in imaging, but existing implementations suffer from two key limitations: $(i)$ the prior density is represented implicitly, and $(ii)$ they rely…
We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to…
So far, the pseudo cross-variogram is primarily used as a tool for the structural analysis of multivariate random fields. Mainly applying recent theoretical results on the pseudo cross-variogram, we use it as a cornerstone in the…
This paper is devoted to the problem of sampling Gaussian fields in high dimension. Solutions exist for two specific structures of inverse covariance : sparse and circulant. The proposed approach is valid in a more general case and…
There has been widespread use of causal inference methods for the rigorous analysis of observational studies and to identify policy evaluations. In this article, we consider a class of generalized coarsened procedures for confounding. At a…
Consistent coupling of effective field theories with a quantum theory of gravity appears to require bounds on the the rank of the gauge group and the amount of matter. We consider landscapes of field theories subject to such to boundedness…
We consider the problem of removing the divergences in an arbitrary gauge-field theory (possibly nonrenormalizable). We show that this can be achieved by performing, order by order in the loop expansion, a redefinition of some parameters…
We study a generalization of higher gauge theory which makes use of generalized geometry and seems to be closely related to double field theory. The local kinematical data of this theory is captured by morphisms of graded manifolds between…
The generalized metric is a T-duality covariant symmetric matrix constructed from the metric and two-form gauge field and arises in generalized geometry. We view it here as a metric on the doubled spacetime and use it to give a simple…
The basis for the field theory are properties of the closed exterior differential forms (skew-symmetric differential forms defined on manifolds with the closed metric forms), which reflect properties of the conservation laws for physical…
A basic problem of classical field theory, which has attracted growing attention over the past decade, is to find and classify all nonlinear deformations of linear abelian gauge theories. The first part of this paper summarizes and…
Rich out of equilibrium collective dynamics of strongly interacting large assemblies emerge in many areas of science. Some intriguing and not fully understood examples are the glassy arrest in atomic, molecular or colloidal systems,…
An approach to the foundations of quantum theory is advertised that proceeds by "reverse engineering" quantum field theory. As a concrete instance of this approach, the general boundary formulation of quantum theory is outlined.
The averaging problem in general relativity is briefly discussed. A new setting of the problem as that of macroscopic description of gravitation is proposed. A covariant space-time averaging procedure is described. The structure of the…
Two very basic constructions involving experimental procedures are the formation of coarse-grained versions of experiments, and the formation of branching sequential experiments. The latter allow for the conditioning of states on the…
Continuous-time Bayesian networks is a natural structured representation language for multicomponent stochastic processes that evolve continuously over time. Despite the compact representation, inference in such models is intractable even…