Related papers: Paracontrolled calculus and regularity structures
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
While a mature body of work supports the study of rewriting systems, abstract tools for Probabilistic Rewriting are still limited. In this paper we study the question of uniqueness of the result (unique limit distribution), and develop a…
In the present paper, we introduce a multi-type calculus for the logic of measurable Kleene algebras, for which we prove soundness, completeness, conservativity, cut elimination and subformula property. Our proposal imports ideas and…
We investigate the relation between the backward uniqueness and the regularity of the coefficients for a parabolic operator. A necessary and sufficient condition for uniqueness is given in terms of the modulus of continuity of the…
A quantization over a manifold can be seen as a way to construct a differential operator with prescribed principal symbol. The quantization map is moreover required to be a linear bijection. It is known that there is in general no natural…
In this paper, we provide a complete regularity analysis for an abstract system of coupled hyperbolic and parabolic equations in a complex Hilbert space. We are able to decompose the unit square of the parameters into three parts where the…
An approach to stabilization of control systems with ultimately wide ranges of uncertainly disturbed parameters is offered. The method relies on using of nonlinear structurally stable functions from catastrophe theory as controllers.…
We introduce the notion of Ricci-corrected differentiation in parabolic geometry, which is a modification of covariant differentiation with better transformation properties. This enables us to simplify the explicit formulae for standard…
Much of the controversy about methods for automated decision making has focused on specific calculi for combining beliefs or propagating uncertainty. We broaden the debate by (1) exploring the constellation of secondary tasks surrounding…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
Many studies have been conducted on statistical convergence, and it remains an area of active research. Since its introduction, statistical convergence has found applications many fields. Nevertheless, there is a shortage of research…
We consider continuous structures which are obtained from finite dimensional Hilbert spaces over $\mathbb{C}$ by adding some unitary operators. Quantum automata and quantum circuits are naturally interpretable in such structures. We…
Eigenstates of the parabose and parafermi creation operators are constructed. In the Dirac contour representation, the parabose eigenstates correspond to the dual vectors of the parabose coherent states. In order $p=2$, conserved-charge…
Despite significant recent advances in the regularity theory for obstacle problems with integro-differential operators, some fundamental questions remained open. On the one hand, there was a lack of understanding of parabolic problems with…
This paper is the first of two papers constructing a calculus of pseudodifferential operators suitable for doing analysis on Q-rank 1 locally symmetric spaces and Riemannian manifolds generalizing these. This generalization is the interior…
Graph rewrite formalisms are a powerful approach to modeling complex molecular systems. They capture the intrinsic concurrency of molecular interactions, thereby enabling a formal notion of mechanism (a partially ordered set of events) that…
We review, for a general audience, a variety of recent experiments on extracting structure from machine-learning mathematical data that have been compiled over the years. Focusing on supervised machine-learning on labeled data from…
In this work we prove convergence of renormalised models in the framework of regularity structures [Hai14] for a wide class of variable coefficient singular SPDEs in their full subcritical regimes. In particular, we provide for the first…
The main goal is to classify 4-dimensional real Lie algebras $\g$ which admit a para-hypercomplex structure. This is a step toward the classification of Lie groups admitting the corresponding left-invariant structure and therefore…
The relation between renormalization and short distance singular divergencies in quantum field theory is studied. As a consequence a finite theory is presented. It is shown that these divergencies are originated by the multiplication of…