Related papers: A tree-free approach to regularity structures: The…

In this letter, we introduce a new approach to formulate the family structure of the standard model. Trying to mimic the highly contrained representation structure of the standard model while extending the symmetry, we propose a…

We study almost minimizers for the thin obstacle problem with variable H\"older continuous coefficients and zero thin obstacle and establish their $C^{1,\beta}$ regularity on the either side of the thin space. Under an additional assumption…

We consider the problem of structure recovery in a graphical model of a tree where some variables are latent. Specifically, we focus on the Gaussian case, which can be reformulated as a well-studied problem: recovering a semi-labeled tree…

Let G be a finite graph with the non-k-order property (essentially, a uniform finite bound on the size of an induced sub-half-graph). A major result of the paper applies model-theoretic arguments to obtain a stronger version of…

We define a natural notion of higher order stability and show that subsets of $\mathbb{F}_p^n$ that are tame in this sense can be approximately described by a union of low-complexity quadratic varieties, up to linear error. This generalizes…

We define and study a model of winding for non-colliding particles in finite trees. We prove that the asymptotic behavior of this statistic satisfies a central limiting theorem, analogous to similar results on winding of bounded particles…

We construct a piecewise linear approximation for the dynamical $\Phi_3^4$ model on $\mathbb{T}^3$ by the theory of regularity structures in [Hai14]. For the dynamical $\Phi^4_3$ model it is proved in [Hai14] that a renormalisation has to…

We construct exact, regular and topologically non-trivial\ configurations of the coupled Einstein-nonlinear sigma model in (3+1) dimensions. The ansatz for the nonlinear $SU(2)$ field is regular everywhere and circumvents Derrick's theorem…

In this paper, we consider the KPZ equation driven by space-time white noise replaced with its fractional derivatives of order $\gamma>0$ in spatial variable. A well-posedness theory for the KPZ equation is established by Hairer [3] as an…

The paper deals with two issues: the existence of universal models of a theory T and related properties when cardinal arithmetic does not give this existence offhand. In the first section we prove that simple theories (e.g., theories…

We consider systems of stochastic evolutionary equations of the type $$du=\mathrm{div}\,S(\nabla u)\,dt+\Phi(u)dW_t$$ where $S$ is a non-linear operator, for instance the $p$-Laplacian $$S(\xi)=(1+|\xi|)^{p-2}\xi,\quad \xi\in\mathbb…

Let $k$ be a field of characteristic $0$, let $\mathsf{C}$ be a finite split category, let $\alpha$ be a 2-cocycle of $\mathsf{C}$ with values in the multiplicative group of $k$, and consider the resulting twisted category algebra…

In this paper we study some properties of the class of nu-quasi-ordinary hypersurface singularities. They are defined by a very mild condition on its (projected) Newton polygon. We associate with them a Newton tree and characterize…

We study various types of consistency of honest decision trees and random forests in the regression setting. In contrast to related literature, our proofs are elementary and follow the classical arguments used for smoothing methods. Under…

Model-free forecasting of the temporal evolution of chaotic systems is crucial but challenging. Existing solutions require hyperparameter tuning, significantly hindering their wider adoption. In this work, we introduce a tree-based approach…

In these notes, we provide an introduction to a new regularity structure used for solving rough mean-field equations. The index set of this regularity structure is described a collection of novel objects which we refer to as Lions trees.…

A general nonlinear regularity model for a set-valued mapping $F:X\times R_+\rightrightarrows Y$, where $X$ and $Y$ are metric spaces, is considered using special iteration procedures, going back to Banach, Schauder, Lusternik and Graves.…

This paper presents a new approach for trees-based regression, such as simple regression tree, random forest and gradient boosting, in settings involving correlated data. We show the problems that arise when implementing standard…

We examine boundary regularity for a fully nonlinear free transmission problem. We argue using approximation methods, comparing the operators driving the problem with a limiting profile. Working natural conditions on the data of the…

Akama et al. [1] introduced a hierarchical classification of first-order formulas for a hierarchical prenex normal form theorem in semi-classical arithmetic. In this paper, we give a justification for the hierarchical classification in a…