Related papers: Fourier transform inequalities for phylogenetic tr…
In evolutionary biology, genetic sequences carry with them a trace of the underlying tree that describes their evolution from a common ancestral sequence. The question of how many sequence sites are required to recover this evolutionary…
Phylogenetic networks play an important role in evolutionary biology as, other than phylogenetic trees, they can be used to accommodate reticulate evolutionary events such as horizontal gene transfer and hybridization. Recent research has…
Graph invariants are a useful tool in graph theory. Not only do they encode useful information about the graphs to which they are associated, but complete invariants can be used to distinguish between non-isomorphic graphs. Polynomial…
The site frequency spectrum (SFS) is a widely used summary statistic of genomic data. Motivated by recent evidence for the role of neutral evolution in cancer, we investigate the SFS of neutral mutations in an exponentially growing…
The comprehensive characterization of the structure of complex networks is essential to understand the dynamical processes which guide their evolution. The discovery of the scale-free distribution and the small world property of real…
Mutations of genetic sequences are often accompanied by their recombinations, known as phylogenetic networks. These networks are typically reconstructed from coalescent processes that may arise from optimal merging or fitting together a…
Genotype-to-phenotype mappings translate genotypic variations such as mutations into phenotypic changes. Neutrality is the observation that some mutations do not lead to phenotypic changes. Studying the search trajectories in genotypic and…
Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…
We study distorted metrics on binary trees in the context of phylogenetic reconstruction. Given a binary tree $T$ on $n$ leaves with a path metric $d$, consider the pairwise distances $\{d(u,v)\}$ between leaves. It is well known that these…
Many classes of phylogenetic networks have been proposed in the literature. A feature of several of these classes is that if one restricts a network in the class to a subset of its leaves, then the resulting network may no longer lie within…
The integration of Fourier transform and deep learning opens new avenues for time series forecasting. We reconsider the Fourier transform from a basis functions perspective. Specifically, the real and imaginary parts of the frequency…
Phylogenetic trees illustrate the evolutionary history of genes and species. In most cases, although genes evolve along with the species they belong to, a species tree and gene tree are not identical, because of evolutionary events at the…
Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted…
Many hard graph problems can be solved efficiently when restricted to graphs of bounded treewidth, and more generally to graphs of bounded clique-width. But there is a price to be paid for this generality, exemplified by the four problems…
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 the role of phylogenetic trees on correlations in mutation processes. Generally, correlations decay exponentially with the generation number. We find that two distinct regimes of behavior exist. For mutation rates smaller than a…
This paper provides new sufficient and necessary conditions for the frame property of generalized translation-invariant systems. The conditions are formulated in the Fourier domain and consists of estimates involving the upper and lower…
Phylogenetic trees are important tools in the study of evolutionary relationships between species. Measures such as the index of Sackin, Colless, and Total Cophenetic have been extensively used to quantify tree balance, one key property of…
In evolutionary studies it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has…
Fixed tree topologies are widely used in phylodynamic analyses to reduce computational burden, yet the consequences of this assumption remain insufficiently understood. Here, we systematically assess the impact of various fixed-topology…