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Register a new userQuantifying Reticulation in Phylogenetic Complexes Using Homology
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Reticulate evolutionary processes result in phylogenetic histories that cannot be modeled using a tree topology. Here, we apply methods from topological data analysis to molecular sequence data with reticulations. Using a simple example, we demonstrate the correspondence between nontrivial higher homology and reticulate evolution. We discuss the sensitivity of the standard filtration and show cases where reticulate evolution can fail to be detected. We introduce an extension of the standard framework and define the median complex as a construction to recover signal of the frequency and scale of reticulate evolution by inferring and imputing putative ancestral states. Finally, we apply our methods to two datasets from phylogenetics. Our work expands on earlier ideas of using topology to extract important evolutionary features from genomic data.
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Methods for resolving the 3D microstructure of the brain typically start by thinly slicing and staining the brain, and then imaging each individual section with visible light photons or electrons. In contrast, X-rays can be used to image thick samples, providing a rapid approach for producing large 3D brain maps without sectioning. Here we demonstrate the use of synchrotron X-ray microtomography ($mu$CT) for producing mesoscale $(1~mu m^3)$ resolution brain maps from millimeter-scale volumes of mouse brain. We introduce a pipeline for $mu$CT-based brain mapping that combines methods for sample preparation, imaging, automated segmentation of image volumes into cells and blood vessels, and statistical analysis of the resulting brain structures. Our results demonstrate that X-ray tomography promises rapid quantification of large brain volumes, complementing other brain mapping and connectomics efforts.
Tree-child networks, one of the prominent network classes in phylogenetics, have been introduced for the purpose of modeling reticulate evolution. Recently, the first author together with Gittenberger and Mansouri (2019) showed that the number ${rm TC}_{ell,k}$ of tree-child networks with $ell$ leaves and $k$ reticulation vertices has the first-order asymptotics [ {rm TC}_{ell,k}sim c_kleft(frac{2}{e}right)^{ell}ell^{ell+2k-1},qquad (ellrightarrowinfty). ] Moreover, they also computed $c_k$ for $k=1,2,$ and $3$. In this short note, we give a second approach to the above result which is based on a recent (algorithmic) approach for the counting of tree-child networks due to Cardona and Zhang (2020). This second approach is also capable of giving a simple, closed-form expression for $c_k$ for all $kgeq 0$.
Deficient myelination of the brain is associated with neurodevelopmental delays, particularly in high-risk infants, such as those born small in relation to their gestational age (SGA). New methods are needed to further study this condition. Here, we employ Color Spatial Light Interference Microscopy (cSLIM), which uses a brightfield objective and RGB camera to generate pathlength-maps with nanoscale sensitivity in conjunction with a regular brightfield image. Using tissue sections stained with Luxol Fast Blue, the myelin structures were segmented from a brightfield image. Using a binary mask, those portions were quantitatively analyzed in the corresponding phase maps. We first used the CLARITY method to remove tissue lipids and validate the sensitivity of cSLIM to lipid content. We then applied cSLIM to brain histology slices. These specimens are from a previous MRI study, which demonstrated that appropriate for gestational age (AGA) piglets have increased internal capsule myelination (ICM) compared to small for gestational age (SGA) piglets and that a hydrolyzed fat diet improved ICM in both. The identity of samples was blinded until after statistical analyses.
In previous work, we gave asymptotic counting results for the number of tree-child and normal networks with $k$ reticulation vertices and explicit exponential generating functions of the counting sequences for $k=1,2,3$. The purpose of this note is two-fold. First, we make some corrections to our previous approach which overcounted the above numbers and thus gives erroneous exponential generating functions (however, the overcounting does not effect our asymptotic counting results). Secondly, we use our (corrected) exponential generating functions to derive explicit formulas for the number of tree-child and normal networks with $k=1,2,3$ reticulation vertices. This re-derives recent results of Carona and Zhang, answers their question for normal networks with $k=2$, and adds new formulas in the case $k=3$.
Obstructive sleep Apnea (OSA) is a form of sleep disordered breathing characterized by frequent episodes of upper airway collapse during sleep. Pediatric OSA occurs in 1-5% of children and can related to other serious health conditions such as high blood pressure, behavioral issues, or altered growth. OSA is often diagnosed by studying the patients sleep cycle, the pattern with which they progress through various sleep states such as wakefulness, rapid eye-movement, and non-rapid eye-movement. The sleep state data is obtained using an overnight polysomnography test that the patient undergoes at a hospital or sleep clinic, where a technician manually labels each 30 second time interval, also called an epoch, with the current sleep state. This process is laborious and prone to human error. We seek an automatic method of classifying the sleep state, as well as a method to analyze the sleep cycles. This article is a pilot study in sleep state classification using two approaches: first, well use methods from the field of topological data analysis to classify the sleep state and second, well model sleep states as a Markov chain and visually analyze the sleep patterns. In the future, we will continue to build on this work to improve our methods.
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