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Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees, such as hybridization, introgression, and lateral gene transfer. Studying phylogenetic networks under a statistical model of DNA…

We define a new topological invariant of line arrangements in the complex projective plane. This invariant is a root of unity defined under some combinatorial restrictions for arrangements endowed with some special torsion character on the…

Modern deep learning usually treats models as separate artifacts: trained independently, specialized for particular purposes, and replaced when improved versions appear. This thesis studies model merging as an alternative paradigm:…

This article proposes a novel approach to statistical alignment of nucleotide sequences by introducing a context dependent structure on the substitution process in the underlying evolutionary model. We propose to estimate alignments and…

Network inference is a rapidly advancing field, with new methods being proposed on a regular basis. Understanding the advantages and limitations of different network inference methods is key to their effective application in different…

Motivation: Word-based or `alignment-free' methods for phylogeny reconstruction are much faster than traditional approaches, but they are generally less accurate. Most of these methods calculate pairwise distances for a set of input…

An attempt to use phylogenetic invariants for tree reconstruction was made at the end of the 80s and the beginning of the 90s by several authors (the initial idea due to Lake and Cavender and Felsenstein in 1987. However, the efficiency of…

We consider the problem of estimating the topology of multiple networks from nodal observations, where these networks are assumed to be drawn from the same (unknown) random graph model. We adopt a graphon as our random graph model, which is…

The latent space model is one of the well-known methods for statistical inference of network data. While the model has been much studied for a single network, it has not attracted much attention to analyze collectively when multiple…

We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…

We present a same-level comparison of the most prominent inversion methods for the reconstruction of the matter density field in the quasi-linear regime from the Ly$\alpha$ forest flux. Moreover, we present a pathway for refining the…

This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also…

Data-driven constitutive modeling frameworks based on neural networks and classical representation theorems have recently gained considerable attention due to their ability to easily incorporate constitutive constraints and their excellent…

Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard…

Subtle alterations in brain network topology often evade detection by traditional statistical methods. To address this limitation, we introduce a Bayesian inference framework for topological comparison of brain networks that…

Mixed-effects models are among the most commonly used statistical methods for the exploration of multispecies data. In recent years, also Joint Species Distribution Models and Generalized Linear Latent Variale Models have gained in…

More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…

The systems without symmetries, e.g. the spatial and chiral symmetries, are generally thought to be improper for topological study and no conventional integral topological invariant can be well defined. In this work, with multi-band…

We examine a mathematical question concerning the reconstruction accuracy of the Fitch algorithm for reconstructing the ancestral sequence of the most recent common ancestor given a phylogenetic tree and sequence data for all taxa under…

A systematic assessment of global neural network connectivity through direct electrophysiological assays has remained technically unfeasible even in dissociated neuronal cultures. We introduce an improved algorithmic approach based on…