Related papers: Markov invariants, plethysms, and phylogenetics (t…
Using the Fredholm setup of [12], we study genus zero (and higher) relative Gromov-Witten invariants with maximum tangency of symplectic log Calabi-Yau fourfolds. In particular, we give a short proof of [23, Conjecture 6.2] that expresses…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
The transition matrix of a Markov chain $(X_k,k\geq 0)$ on a finite or infinite rooted tree is said to be almost upper-directed if, given $X_k$, the node $X_{k+1}$ is either a descendant of $X_k$ or the parent of $X_k$. It is said to be…
We propose a statistical method to test whether two phylogenetic trees with given alignments are significantly incongruent. Our method compares the two distributions of phylogenetic trees given by the input alignments, instead of comparing…
We introduce a probabilistic framework for two-sample comparison based on a nonparametric process taking the form of a Markov model that transitions between a "divide" and a "merge" state on a multi-resolution partition tree of the sample…
Conditional independence and Markov properties are powerful tools allowing expression of multidimensional probability distributions by means of low-dimensional ones. As multidimensional possibilistic models have been studied for several…
Hidden Markov Models (HMMs) are powerful tools for modeling sequential data, where the underlying states evolve in a stochastic manner and are only indirectly observable. Traditional HMM approaches are well-established for linear sequences,…
Phylogenetic trees are a central tool in understanding evolution. They are typically inferred from sequence data, and capture evolutionary relationships through time. It is essential to be able to compare trees from different data sources…
We study symmetries of bases and spanning sets in finite element exterior calculus, using representation theory. We want to know which vector-valued finite element spaces have bases invariant under permutation of vertex indices. The…
Statistical dependencies among wavelet coefficients are commonly represented by graphical models such as hidden Markov trees(HMTs). However, in linear inverse problems such as deconvolution, tomography, and compressed sensing, the presence…
We analyse the structure of imprecise Markov chains and study their convergence by means of accessibility relations. We first identify the sets of states, so-called minimal permanent classes, that are the minimal sets capable of containing…
The search for similarity and dissimilarity measures on phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in phylogenetic databases, and the assessment of clustering results in…
We study existence and uniqueness of invariant probability measures for continuous-time Markov processes on general state spaces. Existence is obtained from tightness of time averages under a weak regularity assumption inspired by…
Loop invariants are software properties that hold before and after every iteration of a loop. As such, invariants provide inductive arguments that are key in automating the verification of program loops. The problem of generating loop…
We give a new, two-step approach to prove existence of finite invariant measures for a given Markovian semigroup. First, we identify a convenient auxiliary measure and then we prove conditions equivalent to the existence of an invariant…
Phylogenetic networks are rooted acyclic directed graphs in which the leaves are identified with members of a set X of species. The cluster of a vertex is the set of leaves that are descendants of the vertex. A network is "distinct-cluster"…
The spanning tree heuristic is a commonly adopted procedure in network inference and estimation. It allows one to generalize an inference method developed for trees, which is usually based on a statistically rigorous approach, to a…
Cyclically ordered graphs, or cogs, sit between abstract graphs and cellularly embedded graphs. They arise naturally in topological graph theory, knot theory, and mathematical biology. We develop a formal theory of cogs and establish a…
DAG models are statistical models satisfying a collection of conditional independence relations encoded by the nonedges of a directed acyclic graph (DAG) $\mathcal{G}$. Such models are used to model complex cause-effect systems across a…
We study various classes of random processes defined on the regular tree $T_d$ that are invariant under the automorphism group of $T_d$. Most important ones are factor of i.i.d. processes (randomized local algorithms), branching Markov…