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Dual-tree wavelet decompositions have recently gained much popularity, mainly due to their ability to provide an accurate directional analysis of images combined with a reduced redundancy. When the decomposition of a random process is…
Let $\mathcal{L}(T,\lambda)=\sum_{k=0}^n(-1)^{k}c_{k}(T)\lambda^{n-k}$ be the characteristic polynomial of its Laplacian matrix of a tree $T$. This paper studied some properties of the generating function of the coefficients sequence $(c_0,…
The sample frequency spectrum of a segregating site is the probability distribution of a sample of alleles from a genetic locus, conditional on observing the sample to have more than one clearly different phenotypes. We present a model for…
The reconstruction of large phylogenetic trees from data that violates clocklike evolution (or as a supertree constructed from any m input trees) raises a difficult question for biologists - how can one assign relative dates to the vertices…
Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. Here we…
New representations of tree-structured data objects, using ideas from topological data analysis, enable improved statistical analyses of a population of brain artery trees. A number of representations of each data tree arise from…
We apply recently developed inference methods based on general coalescent processes to DNA sequence data obtained from various marine species. Several of these species are believed to exhibit so-called shallow gene genealogies, potentially…
Empirical observations suggest that in pure even-aged forests, the mean diameter of forest trees (D, diameter at breast height, 1.3 m above ground) tends to remain a constant proportion of stand height (H, average height of the largest…
Multiple-merger coalescents, e.g. $\Lambda$-$n$-coalescents, have been proposed as models of the genealogy of $n$ sampled individuals for a range of populations whose genealogical structures are not captured well by Kingman's…
Merge trees, a type of topological descriptor, serve to identify and summarize the topological characteristics associated with scalar fields. They present a great potential for the analysis and visualization of time-varying data. First,…
Phylogenetic trees play a key role in the reconstruction of evolutionary relationships. Typically, they are derived from aligned sequence data (like DNA, RNA, or proteins) by using optimization criteria like, e.g., maximum parsimony (MP).…
The genetic diversity of a species is shaped by its recent evolutionary history and can be used to infer demographic events or selective sweeps. Most inference methods are based on the null hypothesis that natural selection is a weak or…
The observed sequence variation at a locus informs about the evolutionary history of the sample and past population size dynamics. The Kingman coalescent is used in a generative model of molecular sequence variation to infer evolutionary…
The multi-species coalescent provides an elegant theoretical framework for estimating species trees and species demographics from genetic markers. Practical applications of the multi-species coalescent model are, however, limited by the…
Phylogenetic networks are a special type of graph which generalize phylogenetic trees and that are used to model non-treelike evolutionary processes such as recombination and hybridization. In this paper, we consider {\em unrooted}…
Collaborations and citations within scientific research grow simultaneously and interact dynamically. Modelling the coevolution between them helps to study many phenomena that can be approached only through combining citation and…
For a family of models of evolving population under selection, which can be described by noisy traveling wave equations, the coalescence times along the genealogical tree scale like $\log^\alpha N$, where $N$ is the size of the population,…
The Hill coefficient is often used as a direct measure of the cooperativity of binding processes. It is an essential tool for probing properties of reactions in many biochemical systems. Here we analyze existing experimental data and…
We present Collaborative Trees, a novel tree model designed for regression prediction, along with its bagging version, which aims to analyze complex statistical associations between features and uncover potential patterns inherent in the…
Positive selection distorts the structure of genealogies and hence alters patterns of genetic variation within a population. Most analyses of these distortions focus on the signatures of hitchhiking due to hard or soft selective sweeps at a…