Related papers: Global smoothing of a subanalytic set

We propose a new exact approach to the generalized graph layering problem that is based on a particular quadratic assignment formulation. It expresses, in a natural way, the associated layout restrictions and several possible objectives,…

In this paper, we study formal mappings between smooth generic submanifolds in multidimensional complex space and establish results on finite determination, convergence and local biholomorphic and algebraic equivalence. Our finite…

Consider the equivariant wave map equation from Minkowski space to a rotationnally symmetric manifold which has an equator (example: the sphere). In dimension 3, this article gives a necessary and sufficient condition for the existence of a…

Forecast verification plays a crucial role in the development cycle of operational numerical weather prediction models. At the same time, verification remains a challenge as the traditionally used non-spatial forecast quality metrics…

We present a generic construction of finite realisations of amalgamation patterns. An amalgamation pattern is specified by a finite collection of finite template structures together with a collection of partial isomorphisms between them. A…

These notes constitute a survey on the geometric properties of globally subanalytic sets. We start with their definition and some fundamental results such as Gabrielov's Complement Theorem or existence of cell decompositions. We then give…

We show that the global and local constructions of three types of blowup of a smooth manifold along a closed submanifold in differential topology are equivalent.

In this paper we introduce the notion of cofrontal mappings, as the dual objects to frontal mappings, and study their basic local and global properties. Cofrontals are very special mappings and far from generic nor stable except for the…

Spherically symmetric solutions of generic gravitational models are optimally, and legitimately, obtained by expressing the action in terms of the two surviving metric components. This shortcut is not to be overdone, however: a one-function…

Suppose that $C=(C_1,..., C_m)$ is a configuration of 2-dimensional symplectic submanifolds in a symplectic 4-manifold $(X,\omega)$ with connected, negative definite intersection graph $\Gamma_C$. We show that by replacing an appropriate…

We study the analytic and topological invariants associated with complex normal surface singularities. Our goal is to provide topological formulae for several discrete analytic invariants whenever the analytic structure is generic (with…

It is shown that if the system of the Euler equations has a special global in time smooth solution with the linear profile of velocity, then another solutions with Cauchy data, close in the Sobolev norm to the initial data of the given…

We discuss the local and global problems for the equivalence of geometric structures of an arbitrary order and, in later sections, attention is given to what really matters, namely the equivalence with respect to transformations belonging…

Probabilistic smoothing is a standard tool for global optimization, but existing methods rely on Gaussian kernels and specific transforms, often resulting in strong hyperparameter sensitivity and limited robustness. We propose a general…

Two core challenges of alignment are 1) scalable oversight and 2) accounting for the dynamic nature of human values. While solutions like recursive reward modeling address 1), they do not simultaneously account for 2). We sketch a roadmap…

Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…

We present a computational scheme that derives a global polynomial level set parametrisation for smooth closed surfaces from a regular surface-point set and prove its uniqueness. This enables us to approximate a broad class of smooth…

In this paper, we extend the previous convergence results for the generalized alternating projection method applied to subspaces in [arXiv:1703.10547] to hold also for smooth manifolds. We show that the algorithm locally behaves similarly…

We construct a generalization of the Dolbeault-Grothendieck resolution on a singular complex space. The same construction yields, for each morphism of analytic spaces, a pullback mapping between the respective Dolbeault-Grothendieck…

We construct standard resolutions for analytic local modules on complex hypersurfaces using standard basis methods, with extensions to complete intersections. The algebraic version over arbitrary infinite fields is also suggested.…