Related papers: Every cutoff profile is possible

We establish necessary and sufficient conditions for consistent root reconstruction in continuous-time Markov models with countable state space on bounded-height trees. Here a root state estimator is said to be consistent if the probability…

We prove that every amenable one-ended Cayley graph has an invariant spanning tree of one end. More generally, for any 1-ended amenable unimodular random graph we construct a factor of iid percolation (jointly unimodular subgraph) that is…

Consider a Markov chain on the space of rooted real binary trees that randomly removes leaves and reinserts them on a random edge and suitably rescales the lengths of edges. This chain was introduced by David Aldous who conjectured a…

A discrete-time Markov chain can be transformed into a new Markov chain by looking at its states along iterations of an almost surely finite stopping time. By the optional stopping theorem, any bounded harmonic function with respect to the…

The MULTICUT problem, given a graph G, a set of terminal pairs T={(s_i,t_i) | 1 <= i <= r} and an integer p, asks whether one can find a cutset consisting of at most p non-terminal vertices that separates all the terminal pairs, i.e., after…

We present a new perfect simulation algorithm for stationary chains having unbounded variable length memory. This is the class of infnite memory chains for which the family of transition probabilities is represented by a probabilistic…

The $k$-cut number of rooted graphs was introduced by Cai et al. as a generalization of the classical cutting model by Meir and Moon. In this paper, we show that all moments of the k-cut number of conditioned Galton-Watson trees converges…

The first part of this paper ( arXiv:1607.02114 ) introduced splitting trees, those chronological trees admitting the self-similarity property where individuals give birth, at constant rate, to iid copies of themselves. It also established…

We prove that every graph has a canonical tree of tree-decompositions that distinguishes all principal tangles (these include the ends and various kinds of large finite dense structures) efficiently. Here `trees of tree-decompositions' are…

A new Bayesian modelling framework is introduced for piece-wise homogeneous variable-memory Markov chains, along with a collection of effective algorithmic tools for change-point detection and segmentation of discrete time series. Building…

Markov decision processes (MDPs) describe sequential decision-making processes; MDP policies return for every state in that process an advised action. Classical algorithms can efficiently compute policies that are optimal with respect to,…

In this article, we considers reversible Markov chains of which $L^2$-distances can be expressed in terms of Laplace transforms. The cutoff of Laplace transforms was first discussed by Chen and Saloff-Coste in [8], while we provide here a…

We study convergence to equilibrium for a large class of Markov chains in random environment. The chains are sparse in the sense that in every row of the transition matrix $P$ the mass is essentially concentrated on few entries. Moreover,…

The Markov Chain Tree Theorem is extended to the max algebra and possible applications to ranking problems are discussed.

The concepts of probability, statistics and stochastic theory are being successfully used in structural engineering. Markov Chain modelling is a simple stochastic process model that has found its application in both describing stochastic…

Hidden tree Markov models allow learning distributions for tree structured data while being interpretable as nondeterministic automata. We provide a concise summary of the main approaches in literature, focusing in particular on the…

The Pathwidth Theorem states that if a class of graphs has unbounded pathwidth, then it contains all trees as graph minors. We prove a similar result for dense graphs. More precisely, we give a finite family of tree-like patterns and prove…

We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in…

We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm…

This simple note lays out a few observations which are well known in many ways but may not have been said in quite this way before. The basic idea is that when comparing two different Markov chains it is useful to couple them is such a way…