Related papers: A down-up chain with persistent labels on multifur…
A theory of symbolic dynamic systems with long-range correlations based on the consideration of the binary N-step Markov chains developed earlier in Phys. Rev. Lett. 90, 110601 (2003) is generalized to the biased case (non equal numbers of…
We define the beta diffusion tree, a random tree structure with a set of leaves that defines a collection of overlapping subsets of objects, known as a feature allocation. A generative process for the tree structure is defined in terms of…
We study Markov chains for $\alpha$-orientations of plane graphs, these are orientations where the outdegree of each vertex is prescribed by the value of a given function $\alpha$. The set of $\alpha$-orientations of a plane graph has a…
We provide a probabilistic analysis of the upwind scheme for multi-dimensional transport equations. We associate a Markov chain with the numerical scheme and then obtain a backward representation formula of Kolmogorov type for the numerical…
We propose a method for the classification of objects that are structured as random trees. Our aim is to model a distribution over the node label assignments in settings where the tree data structure is associated with node attributes…
We explore labeled chip-firing on undirected $k$-ary trees, trees where every vertex has degree $k+1$. First, we extend known results for binary trees from Musiker and Nguyen, including the endgame and the locations of the smallest and…
We study the following growth model on a regular d-ary tree. Points at distance n adjacent to the existing subtree are added with probabilities proportional to alpha^{-n}, where alpha<1 is a positive real parameter. The heights of these…
By rewriting the famous hook-content formula it easily follows that there are $\prod\limits_{1 \le i < j \le n} \frac{k_j - k_i + j -i}{j-i}$ semistandard tableaux of shape $(k_n,k_{n-1},...,k_1)$ with entries in $\{1,2,...,n\}$ or,…
We investigate labeling schemes supporting adjacency, ancestry, sibling, and connectivity queries in forests. In the course of more than 20 years, the existence of $\log n + O(\log \log)$ labeling schemes supporting each of these functions…
We give a short and direct proof of a remarkable identity that arises in the enumeration of labeled trees with respect to their indegree sequence, where all edges are oriented from the vertex with lower label towards the vertex with higher…
There is a well-established theory linking certain semi-Markov chains and continuous-time random walks to time-fractional equations and anomalous diffusion. In this work, we go beyond the semi-Markov framework by considering some…
In this paper, we study a regular rooted coloured tree with random labels assigned to its edges, where the distribution of the label assigned to an edge depends on the colours of its endpoints. We obtain some new results relevant to this…
A finite graph embedded in the plane is called a series-parallel map if it can be obtained from a finite tree by repeatedly subdividing and doubling edges. We study the scaling limit of weighted random two-connected series-parallel maps…
We introduce the notion of a restricted exchangeable partition of $\mathbb{N}$. We obtain integral representations, consider associated fragmentations, embeddings into continuum random trees and convergence to such limit trees. In…
In this paper we consider the problem of graph-based transductive classification, and we are particularly interested in the directed graph scenario which is a natural form for many real world applications. Different from existing research…
A labeling scheme for nearest common ancestors assigns a distinct binary string, called the label, to every node of a tree, so that given the labels of two nodes (and no further information about the topology of the tree) we can compute the…
In this work we introduce and study various generalizations of the notion of increasingly labelled trees, where the label of a child node is always larger than the label of its parent node, to multilabelled tree families, where the nodes in…
In [Aldous,Pitman,1998] a tree-valued Markov chain is derived by pruning off more and more subtrees along the edges of a Galton-Watson tree. More recently, in [Abraham,Delmas,2012], a continuous analogue of the tree-valued pruning dynamics…
Consider longitudinal networks whose edges turn on and off according to a discrete-time Markov chain with exponential-family transition probabilities. We characterize when their joint distributions are also exponential families with the…
In the CHY-frame for the tree-level amplitudes, the bi-adjoint scalar theory has played a fundamental role because it gives the on-shell Feynman diagrams for all other theories. Recently, an interesting generalization of the bi-adjoint…