相关论文: Trees, valuations and the Green-Lazrsfeld set

It is becoming increasingly important for machine learning methods to make predictions that are interpretable as well as accurate. In many practical applications, it is of interest which features and feature interactions are relevant to the…

The aim of these notes is threefold. First, we discuss geometrical aspects of conformal covariance in stochastic Schramm-Loewner evolutions (SLEs). This leads us to introduce new ``dipolar'' SLEs, besides the known chordal, radial or…

Explaining why and how a tree $t$ structurally differs from another tree $t^\star$ is a question that is encountered throughout computer science, including in understanding tree-structured data such as XML or JSON data. In this article, we…

In this survey, we explore the connections between two areas of probability: percolation theory and population genetic models. Our first goal is to highlight a construction on Galton-Watson trees, which has been described in two different…

The Lyubeznik numbers are invariants of a local ring containing a field that capture ring-theoretic properties, but also have numerous connections to geometry and topology. We discuss basic properties of these integer-valued invariants, as…

A tree, embedded into plane, is a dessin d'enfant and its Belyi function is a polynomial --- Shabat polynomial. The Zapponi form of this polynomial is unique, so we can correspond to an embedded tree the Julia set of its Shabat-Zapponi…

This paper treats the variation of sets. We attempt to formulate convergence and continuity of set-valued functions in a different way from the theories on sequences of sets and correspondence. In the final section, we also attempt to…

We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…

We introduce and study in detail the notion of compatibility between valuations and orderings in real hyperfields. We investigate their relation with valuations and orderings induced on factor and residue hyperfields. Much of the theory…

The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…

This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…

In this paper, we unify the study of classical and non-classical algebra-valued models of set theory, by studying variations of the interpretation functions for identity and set-membership. Although, these variations coincide with the…

We establish the existence, uniqueness, and various estimates for Green functions of mixed Dirichlet-conormal derivative problems for the stationary Stokes system with measurable coefficients in a two-dimensional Reifenberg flat domain with…

Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…

We present a graph theoretical approach to the configurational statistics of random tree-like objects, such as randomly branching polymers. In particular, for ideal trees we show that Pr\"ufer labelling provides: (i) direct access to the…

We revisit one of Zilber's early results in model-theoretic algebra, viz. definability in Schur's lemma. This takes place in a broader context than the original version from the seventies. The present exposition contains results extracted…

Consider complex semisimple Lie algebras of a given dimension specified by their structure constants. We describe a finite collection of rational functions in the structure constants that form a complete set of invariants: two sets of…

In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…

The aim of this paper is to show certain properties of the Green's functions related to the Hill's equation coupled with different two point boundary value conditions. We will obtain the expression of the Green's function of Neumann,…

We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to…