Related papers: On Martin's Pointed Tree Theorem

We study weak approximation and the Hilbert property for Campana points, both of importance in recent work on a Manin-type conjecture by Pieropan, Smeets, Tanimoto and Varilly-Alvarado. We show that weak weak approximation implies the…

We present Model Predictive Trees (MPT), a receding horizon tree search algorithm that improves its performance by reusing information efficiently. Whereas existing solvers reuse only the highest-quality trajectory from the previous…

In this paper, we strengthen the splitting theorem proved in [14, 15] and provide a different approach using ideas from the weak KAM theory.

We establish a framework for the study of the effective theory of weak convergence of measures. We define two effective notions of weak convergence of measures on $\mathbb{R}$: one uniform and one non-uniform. We show that these notions are…

We study infinite tree and ultrametric matrices, and their action on the boundary of the tree. For each tree matrix we show the existence of a symmetric random walk associated to it and we study its Green potential. We provide a…

Reverse order law for the Moore-Penrose inverses of tensors are useful in the field of multilinear algebra. In this paper, we first prove some more identities involving the Moore-Penrose inverse of tensors. We then obtain a few necessary…

The inverse problem method is tested for a class of mean field statistical mechanics models representing a mixture of particles of different species. The robustness of the inversion is investigated for different values of the physical…

A tree is pathwise-random if all of its paths are Martin-Lof random. We show that (a) no weakly 2-random real computes a perfect pathwise-random tree; it follows that the class of perfect pathwise-random trees is null, with respect to any…

We prove a structural theorem for generalized arithmetic progressions in $\F_p$ which contain a large product set of two other progressions.

This paper uses the framework of reverse mathematics to investigate the strength of two recurrence theorems of topological dynamics. It establishes that one of these theorems, the existence of an almost periodic point, lies strictly between…

We present, in detail and with a modern rigor, the two title proofs. The Weak Jordan Theorem (WJT) states that the complement of any topological circuit in the plane is disconnected.

A short note on the reverse mathematical status of the totality of the relativised fast growing hierarchy.

Parks introduced a formulation of time dependent weak values in 2008, which is the formalism we use in this paper. In this paper we extend notions from time dependent weak values to show that Hamiltonians associated with weak value…

We present various results concerning the two-weight Hardy's inequality on infinite trees. Our main scope is to survey known characterizations (and proofs) for trace measures, as well as to provide some new ones. Also for some of the known…

A congruence of the weak order is simple if its quotientope is a simple polytope. We provide an alternative elementary proof of the characterization of the simple congruences in terms of forbidden up and down arcs. For this, we provide a…

We study the P versus NP problem through properties of functions and monoids, continuing the work of [3]. Here we consider inverse monoids whose properties and relationships determine whether P is different from NP, or whether injective…

The trace $\tr(q(\ma{L} + q\ma{I})^{-1})$, where $\ma{L}$ is a symmetric diagonally dominant matrix, is the quantity of interest in some machine learning problems. However, its direct computation is impractical if the matrix size is large.…

Reverse Mathematics is a program in the foundations of mathematics which provides an elegant classification of theorems of ordinary mathematics based on computability. Our aim is to provide an alternative classification of theorems based on…

We study the inverse problem of recovering a tree graph together with the weights on its edges (equivalently a metric tree) from the knowledge of the Dirichlet-to-Neumann matrix associated with the Laplacian. We prove an explicit formula…

Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give…