相关论文: Variational Problems for Tree Roots and Branches

Let k be a local field and let A be the two-by-two matrix algebra over k. In our previous work we developed a theory that allows the computation of the set of maximal orders in A containing a given suborder. This set is given as a sub-tree…

We generalize the uniform spanning tree to construct a family of determinantal measures on essential spanning forests on periodic planar graphs in which every component tree is bi-infinite. Like the uniform spanning tree, these measures…

There is an incompatibility between gauge invariance and the semi-classical time-dependent perturbation theory commonly used to calculate light absorption and scattering cross-sections. There is an additional incompatibility between…

We prove a lower bound on the number of spanning two-forests in a graph, in terms of the number of vertices, edges, and spanning trees. This implies an upper bound on the average cut size of a random two-forest. The main tool is an identity…

Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for…

Mathematical modeling is a standard approach to solve many real-world problems and {\em diversity} of solutions is an important issue, emerging in applying solutions obtained from mathematical models to real-world problems. Many studies…

Multi-view learning is a learning task in which data is described by several concurrent representations. Its main challenge is most often to exploit the complementarities between these representations to help solve a…

We consider three bivariate polynomial invariants $P$, $A$, and $S$ for rooted trees, as well as a trivariate polynomial invariant $M$. These invariants are motivated by random destruction processes such as the random cutting model or site…

Decision tree learning is a widely used approach in machine learning, favoured in applications that require concise and interpretable models. Heuristic methods are traditionally used to quickly produce models with reasonably high accuracy.…

We present here a new and universal approach for the study of random and/or trees, unifying in one framework many different models, including some novel ones not yet understood in the literature. An and/or tree is a Boolean expression…

The weighted $3$-Set Packing problem is defined as follows: As input, we are given a collection $\mathcal{S}$ of sets, each of cardinality at most $3$ and equipped with a positive weight. The task is to find a disjoint sub-collection of…

We define a search problem on trees that closely captures the backtracking behavior of all current practical graph isomorphism algorithms. Given two trees with colored leaves, the goal is to find two leaves of matching color, one in each of…

This survey synthesizes the current state of the art on the regularity theory for solutions to the optimal partition problem. Namely, we consider non-negative, vector-valued Sobolev functions whose components have mutually disjoint support,…

We consider two different variational models of transport networks, the so-called branched transport problem and the urban planning problem. Based on a novel relation to Mumford-Shah image inpainting and techniques developed in that field,…

Accessibility percolation is a new type of percolation problem inspired by evolutionary biology. To each vertex of a graph a random number is assigned and a path through the graph is called accessible if all numbers along the path are in…

We study graph estimation and density estimation in high dimensions, using a family of density estimators based on forest structured undirected graphical models. For density estimation, we do not assume the true distribution corresponds to…

We propose a new arithmetic for non-empty rooted unordered trees simply called trees. After discussing tree representation and enumeration, we define the operations of tree addition, multiplication and stretch, prove their properties, and…

We study the effectiveness of subagging, or subsample aggregating, on regression trees, a popular non-parametric method in machine learning. First, we give sufficient conditions for pointwise consistency of trees. We formalize that (i) the…

Fruit monitoring plays an important role in crop management, and rising global fruit consumption combined with labor shortages necessitates automated monitoring with robots. However, occlusions from plant foliage often hinder accurate shape…

We consider the problem of optimal approximation of a target measure by an atomic measure with $N$ atoms, in branched optimal transport distance. This is a new branched transport version of optimal quantization problems. New difficulties…