相关论文: Mumford dendrograms

This paper is devoted to a systematic study of a class of binary trees encoding the structure of rational numbers both from arithmetic and dynamical point of view. The paper is divided into two parts. The first one is a critical review of…

We give a new class of multidimensional $p$-adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that multidimensional $p$-adic version of Lagrange's Theorem holds.

A set of linearly constrained permutation matrices are proposed for constructing a class of permutation codes. Making use of linear constraints imposed on the permutation matrices, we can formulate a minimum Euclidian distance decoding…

We present a semantic parser for Abstract Meaning Representations which learns to parse strings into tree representations of the compositional structure of an AMR graph. This allows us to use standard neural techniques for supertagging and…

In this paper we investigate the use of the concept of tree dimension in Horn clause analysis and verification. The dimension of a tree is a measure of its non-linearity - for example a list of any length has dimension zero while a complete…

In this paper, we introduce TreeCoders, a novel family of transformer trees. We moved away from traditional linear transformers to complete k-ary trees. Transformer blocks serve as nodes, and generic classifiers learn to select the best…

Continued fractions have been long studied due to their strong properties, such as rational approximation. In this extent, their arithmetic over real numbers has represented an intriguing problem throughout the years. In this paper, we…

Let $\{{\cdot},{\cdot}\}_{\boldsymbol{\mathcal{P}}}$ be a variational Poisson bracket in a field model on an affine bundle $\pi$ over an affine base manifold $M^m$. Denote by $\times$ the commutative associative multiplication in the…

P. Broussous and S. Stevens studied maps between enlarged Bruhat-Tits buildings to construct types for p-adic unitary groups. They needed maps which respect the Moy-Prasad filtrations. That property is called (CLF), i.e. compatibility with…

We reduce the problem of constructing asymptotically good tree codes to the construction of triangular totally nonsingular matrices over fields with polynomially many elements. We show a connection of this problem to Birkhoff interpolation…

For a fixed property (graph class) ${\Pi}$, given a graph G and an integer k, the ${\Pi}$-deletion problem consists in deciding if we can turn $G$ into a graph with the property ${\Pi}$ by deleting at most $k$ edges. The ${\Pi}$-deletion…

The aim of this thesis is to present an extension to the string graphs of Dixon, Duncan and Kissinger that allows the finite representation of certain infinite families of graphs and graph rewrite rules, and to demonstrate that a logic can…

Complex systems are usually represented as an intricate set of relations between their components forming a complex graph or network. The understanding of their functioning and emergent properties are strongly related to their structural…

We study the enumeration of spinal tree-child phylogenetic networks, a rigid family of tree-child networks in which all internal vertices lie on a single root--to--leaf path. We provide two complementary combinatorial frameworks. First, we…

Text generation from AMR requires mapping a semantic graph to a string that it annotates. Transformer-based graph encoders, however, poorly capture vertex dependencies that may benefit sequence prediction. To impose order on an encoder, we…

Let p > 2 be a prime. Let Q(zeta) be the p-cyclotomic field. Let pi be the prime ideal of Q(zeta) lying over p. This article aims to describe some pi-adic congruences characterizing the structure of the p-class group and of the unit group…

We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…

A set A of natural numbers is finitely embeddable in another such set B if every finite subset of A has a rightward translate that is a subset of B. This notion of finite embeddability arose in combinatorial number theory, but in this paper…

A notion of branch-width, which generalizes the one known for graphs, can be defined for matroids. We first give a proof of the polynomial time model-checking of monadic second-order formulas on representable matroids of bounded…

We extend our previous computations for the relative positions of branches of quaternions to the case of local fields of even characteristic. This is a key step to understand the set of maximal orders containing a given suborder, which is…