Related papers: Microlocal analysis and beyond

We give a microlocal version of the theorem of iterates in multi-anisotropic Gevrey classes for multi-anisotropic hypoelliptic differential operators

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

The partial least squares procedure was originally developed to estimate the slope parameter in multivariate parametric models. More recently it has gained popularity in the functional data literature. There, the partial least squares…

In recent years there has been interest in the theory of local computation over probabilistic Bayesian graphical models. In this paper, local computation over Bayes linear belief networks is shown to be amenable to a similar approach.…

In this paper, we formally define the concept of shifted contact structures on derived (Artin) stacks and study their local properties in the context of derived algebraic geometry. In this regard, for negatively shifted contact derived…

The mesoscopic concept is applied to the description of microcracked brittle materials. The mesoscopic equations are solved in a special case when the microcracks are developing according to the Rice-Griffith evolution law. The evolution of…

A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between…

Finite linear least squares is one of the core problems of numerical linear algebra, with countless applications across science and engineering. Consequently, there is a rich and ongoing literature on algorithms for solving linear least…

We introduce an original notion of extra-fine sheaf on a topological space, and a variant (hyper-extra-fine) for which \v{C}ech cohomology in strictly positive degree vanishes. We provide a characterization of such sheaves when the…

Designing experiments for generalized linear models is difficult because optimal designs depend on unknown parameters. The local optimality approach is to study the regions in parameter space where a given design is optimal. In many…

Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…

Given a compact symplectic manifold whose symplectic form has integer periods, one associates to it a dg category based on the microlocal analysis according to Kashiwara-Schapira

It is a sequel to (Wu in arXiv:2003.05187). In that paper, we introduce a notion called modified ideal sheaf in order to make an asymptotic estimate for the order of the cohomology group. Here we continue to a general discussion about this…

Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

We report on a detailed numerical study of the evolution of semilocal string networks, based on the largest and most accurate field theory simulations of these objects to date. We focus on the large-scale network properties, confirming…

In this paper we show that states, transitions and behavior of concurrent systems can often be modeled as sheaves over a suitable topological space. In this context, geometric logic can be used to describe which local properties (i.e.…

The concept of typed topological space is introduced, for which open sets in a topology on a finite set will be assigned types (from lattice). The neighborhood system of a point, the closure and the connectedness can be defined according to…

We define the notion of sheaf in the context of doctrines. We prove the associate sheaf functor theorem. We show that grothendieck toposes and toposes obtained by the tripos to topos construction are instances of categories of sheaves for a…

Statistical Topology emerged since topological aspects continue to gain importance in many areas of physics. It is most desirable to study topological invariants and their statistics in schematic models that facilitate the identification of…

We present a perturbative construction of interacting quantum field theories on any smooth globally hyperbolic manifold. We develop a purely local version of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization using…