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Register a new userClassifying sleep states using persistent homology and Markov chain: a Pilot Study
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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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This paper presents a method to identify substructures in NMR spectra of mixtures, specifically 2D spectra, using a bespoke image-based Convolutional Neural Network application. This is done using HSQC and HMBC spectra separately and in combination. The application can reliably detect substructures in pure compounds, using a simple network. It can work for mixtures when trained on pure compounds only. HMBC data and the combination of HMBC and HSQC show better results than HSQC alone.
Persistent Homology is a fairly new branch of Computational Topology which combines geometry and topology for an effective shape description of use in Pattern Recognition. In particular it registers through Betti Numbers the presence of holes and their persistence while a parameter (filtering function) is varied. In this paper, some recent developments in this field are integrated in a k-Nearest Neighbor search algorithm suited for an automatic retrieval of melanocytic lesions. Since long, dermatologists use five morphological parameters (A = Asymmetry, B = Boundary, C = Color, D = Diameter, E = Elevation or Evolution) for assessing the malignancy of a lesion. The algorithm is based on a qualitative assessment of the segmented images by computing both 1 and 2-dimensional Persistent Betti Numbers functions related to the ABCDE parameters and to the internal texture of the lesion. The results of a feasibility test on a set of 107 melanocytic lesions are reported in the section dedicated to the numerical experiments.
Purpose: In this work, we present a collaboration to create a validation dataset of pathologist annotations for algorithms that process whole slide images (WSIs). We focus on data collection and evaluation of algorithm performance in the context of estimating the density of stromal tumor infiltrating lymphocytes (sTILs) in breast cancer. Methods: We digitized 64 glass slides of hematoxylin- and eosin-stained ductal carcinoma core biopsies prepared at a single clinical site. We created training materials and workflows to crowdsource pathologist image annotations on two modes: an optical microscope and two digital platforms. The workflows collect the ROI type, a decision on whether the ROI is appropriate for estimating the density of sTILs, and if appropriate, the sTIL density value for that ROI. Results: The pilot study yielded an abundant number of cases with nominal sTIL infiltration. Furthermore, we found that the sTIL densities are correlated within a case, and there is notable pathologist variability. Consequently, we outline plans to improve our ROI and case sampling methods. We also outline statistical methods to account for ROI correlations within a case and pathologist variability when validating an algorithm. Conclusion: We have built workflows for efficient data collection and tested them in a pilot study. As we prepare for pivotal studies, we will consider what it will take for the dataset to be fit for a regulatory purpose: study size, patient population, and pathologist training and qualifications. To this end, we will elicit feedback from the FDA via the Medical Device Development Tool program and from the broader digital pathology and AI community. Ultimately, we intend to share the dataset, statistical methods, and lessons learned.
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.
We propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of the known stimuli that govern neuron activity, and the corresponding state of the animal throughout the experiment performed. Using a generalized linear model for neuron activity and simple assumptions on the effects of the external stimuli, we infer away any contribution to the observed spike trains by the candidate stimuli. Persistent homology then reveals useful information about any further, unknown, covariates.
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