Related papers: Identifiability in Phylogenetics using Algebraic M…

Phylogenetic trees describe the relationships between species in the evolutionary process, and provide information about the rates of diversification. To understand the mechanisms behind macroevolution, we consider a class of multitype…

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…

Phylogenetic trees are leaf-labelled trees, where the leaves correspond to extant species (taxa), and the internal vertices represent ancestral species. The evolutionary history of a set of species can be explained by more than one…

Algebraic techniques in phylogenetics have historically been successful at proving identifiability results and have also led to novel reconstruction algorithms. In this paper, we study the ideal of phylogenetic invariants of the…

In this paper, we study discrete Lyapunov models, which consist of steady-state distributions of first-order vector autoregressive models. The parameter matrix of such a model encodes a directed graph whose vertices correspond to the…

The alpha model, a parametrized family of probabilities on cladograms (rooted binary leaf labeled trees), is introduced. This model is Markovian self-similar, deletion-stable (sampling consistent), and passes through the Yule, Uniform and…

Structural identifiability is an important property of parametric ODE models. When conducting an experiment and inferring the parameter value from the time-series data, we want to know if the value is globally, locally, or non-identifiable.…

We show that each member of a broad class of Markovian population models induces a unique stochastic process on the space of genealogies. We construct this genealogy process and derive exact expressions for the likelihood of an observed…

Identifiability concerns finding which unknown parameters of a model can be estimated from given input-output data. If some subset of the parameters of a model cannot be determined given input-output data, then we say the model is…

Many computational problems admit fast algorithms on special inputs, however, the required properties might be quite restrictive. E.g., many graph problems can be solved much faster on interval or cographs, or on graphs of small…

The feasibility of uniquely estimating parameters of dynamical systems from observations is a widely discussed aspect of mathematical modelling. Several approaches have been published for analyzing identifiability. However, they are…

Phylogenetic networks are used to represent the evolutionary history of species. They are versatile when compared to traditional phylogenetic trees, as they capture more complex evolutionary events such as hybridization and horizontal gene…

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…

Polyploidy is an important speciation mechanism, particularly in land plants. Allopolyploid species are formed after hybridization between otherwise intersterile parental species. Recent theoretical progress has led to successful…

Designing plausible network models typically requires scholars to form a priori intuitions on the key drivers of network formation. Oftentimes, these intuitions are supported by the statistical estimation of a selection of network evolution…

A (pseudo-)metric $D$ on a finite set $X$ is said to be a `tree metric' if there is a finite tree with leaf set $X$ and non-negative edge weights so that, for all $x,y \in X$, $D(x,y)$ is the path distance in the tree between $x$ and $y$.…

The rates-across-sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is the product of a character-specific scale factor and a…

In this paper we propose a novel approach to identify dynamical systems. The method estimates the model structure and the parameters of the model simultaneously, automating the critical decisions involved in identification such as model…

Machine learning (ML) and deep learning models are extensively used for parameter optimization and regression problems. However, not all inverse problems in ML are ``identifiable,'' indicating that model parameters may not be uniquely…

Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…