Related papers: On the conservative pasting lemma

Let F be a continuous injective map from an open subset of R^n to R^n. Assume that, for infinitely many k>1, F induces a bijection between the rational points of denominator k in the domain and those in the image (the denominator of…

Let E be an unbounded open (or closed) domain in Euclidean space of dimension greater or equal to two. We present conservativeness criteria for (possibly reflected) diffusions with state space E that are associated to fairly general…

We study theories of spaces of random variables: first, we consider random variables with values in the interval $[0,1]$, then with values in an arbitrary metric structure, generalising Keisler's randomisation of classical structures. We…

We study proximal random reshuffling for minimizing the sum of locally Lipschitz functions and a proper lower semicontinuous convex function without assuming coercivity or the existence of limit points. The algorithmic guarantees pertaining…

Semi-Lagrangian schemes have proven to be very efficient to model advection problems. However most semi-Lagrangian schemes are not conservative. Here, a systematic method is introduced in order to enforce the conservative property on a…

The Lovasz Local Lemma [EL75] is a powerful tool to prove the existence of combinatorial objects meeting a prescribed collection of criteria. The technique can directly be applied to the satisfiability problem, yielding that a k-CNF formula…

We propose a new algorithmic framework, called "partial rejection sampling", to draw samples exactly from a product distribution, conditioned on none of a number of bad events occurring. Our framework builds (perhaps surprising) new…

Pandres has developed a theory in which the geometrical structure of a real four-dimensional space-time is expressed by a real orthonormal tetrad, and the group of diffeomorphisms is replaced by a larger group called the conservation group.…

Normalizing flows leverage the Change of Variables Formula (CVF) to define flexible density models. Yet, the requirement of smooth transformations (diffeomorphisms) in the CVF poses a significant challenge in the construction of these…

We present new preservation theorems that semantically characterize the $\exists^k \forall^*$ and $\forall^k \exists^*$ prefix classes of first order logic, for each natural number $k$. Unlike preservation theorems in the literature that…

We prove a quantitative averaging lemma for spatially dependent vector fields. Our proof is based on an iteration of the regularizing operator and some elementary considerations about the local inversion theorem.

We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with $\alpha$-H\"older derivatives (for some $0<\alpha\leq 1$). The smooth approximation is given by means of an…

We derive consistency relations for the late universe (CDM and \Lambda CDM): relations between an n-point function of the density contrast \delta and an (n+1)-point function in the limit in which one of the (n+1) momenta becomes much…

We establish a regularity result for optimal sets of the isoperimetric problem with double density under mild ($\alpha$-)H\"older regularity assumptions on the density functions. Our main Theorem improves some previous results and allows to…

On the one hand, we prove that the spaces of C^1 symplectomorphisms and of C^1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of…

Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…

We give a possible extension for shears and overshears in the case of two non commutative (quaternionic) variables in relation with the associated vector fields and flows. We present a possible definition of volume preserving automorphisms,…

We show how Lasry-Lions's result on regularization of functions defined on $\mathbb{R}^n$ or on Hilbert spaces by sup-inf convolutions with squares of distances can be extended to (finite or infinite dimensional) Riemannian manifolds $M$ of…

The local limit of a quantum field theory on the loop space is studied. It is proved that the invariance of the theory with respect to the group of diffeomorphisms leads to Feynman diagrams convergence in the local limit.

We obtain sharp rotation bounds for homeomorphisms $f:\mathbb{C}\to\mathbb{C}$ whose distortion is in $L^p_{loc}$, $p\geq1$, and whose inverse have controlled modulus of continuity. The motivation to study this class of maps comes from…