CUPOLETS: Chaotic unstable periodic orbits theory and applications

Recent theoretical work suggests that periodic orbits of chaotic systems are a rich source of qualitative information about the dynamical system. The presence of unstable periodic orbits located densely on the attractor is a typical characteristic of chaotic systems. This abundance of unstable periodic orbits can be utilized in a wide variety of theoretical and practical applications [19]. In particular, chaotic communication techniques and methods of controlling chaos depend on this property of chaotic attractors [12, 13]. In the first part of this thesis, a control scheme for stabilizing the unstable periodic orbits of chaotic systems is presented and the properties of these orbits are investigated. The technique allows for creation of thousands of periodic orbits. These approximated chaotic unstable periodic orbits are called cupolets (C&barbelow;haotic U&barbelow;nstable P&barbelow;eriodic O&barbelow;rbit- lets). We show that these orbits can be passed through a phase transformation to a compact cupolet state that possesses a wavelet-like structure and can be used to construct adaptive bases. The cupolet transformation can be regarded as an alternative to Fourier and wavelet transformations. In fact, this new framework provides a continuum between Fourier and wavelet transformations and can be used in variety of applications such as data and music compression, as well as image and video processing. The key point in this method is that all of these different dynamical behaviors are easily accessible via small controls. This technique is implemented in order to produce cupolets which are essentially approximate periodic orbits of the chaotic system. The orbits are produced with small perturbations which in turn suggests that these orbits might not be very far away from true periodic orbits. The controls can be considered as external numerical errors that happen at some points along the computer generated orbits. This raises the question of shadowability of these orbits. It is very interesting to know if there exists a true orbit of the system with a slightly different initial condition that stays close to the computer generated orbit. This true orbit, if it exists, is called a shadow and the computer generated orbit is then said to be shadowable by a true orbit. We will present two general purpose shadowing theorems for periodic and nonperiodic orbits of ordinary differential equations. The theorems provide a way to establish the existence of true periodic and non-periodic orbits near the approximated ones. Both theorems are suitable for computations and the shadowing distances, i.e., the distance between the true orbits and approximated orbits are given by quantities computable form the vector field of the differential equation

Pan-cancer classifications of tumor histological images using deep learning

Histopathological images are essential for the diagnosis of cancer type and selection of optimal treatment. However, the current clinical process of manual inspection of images is time consuming and prone to intra- and inter-observer variability. Here we show that key aspects of cancer image analysis can be performed by deep convolutional neural networks (CNNs) across a wide spectrum of cancer types. In particular, we implement CNN architectures based on Google Inception v3 transfer learning to analyze 27815 H&E slides from 23 cohorts in The Cancer Genome Atlas in studies of tumor/normal status, cancer subtype, and mutation status. For 19 solid cancer types we are able to classify tumor/normal status of whole slide images with extremely high AUCs (0.995±0.008). We are also able to classify cancer subtypes within 10 tissue types with AUC values well above random expectations (micro-average 0.87±0.1). We then perform a cross-classification analysis of tumor/normal status across tumor types. We find that classifiers trained on one type are often effective in distinguishing tumor from normal in other cancer types, with the relationships among classifiers matching known cancer tissue relationships. For the more challenging problem of mutational status, we are able to classify TP53 mutations in three cancer types with AUCs from 0.65-0.80 using a fully-trained CNN, and with similar cross-classification accuracy across tissues. These studies demonstrate the power of CNNs for not only classifying histopathological images in diverse cancer types, but also for revealing shared biology between tumors. We have made software available at: https://github.com/javadnoorb/HistCNNFirst author draf

Deep learning-based cross-classifications reveal conserved spatial behaviors within tumor histological images.

Histopathological images are a rich but incompletely explored data type for studying cancer. Manual inspection is time consuming, making it challenging to use for image data mining. Here we show that convolutional neural networks (CNNs) can be systematically applied across cancer types, enabling comparisons to reveal shared spatial behaviors. We develop CNN architectures to analyze 27,815 hematoxylin and eosin scanned images from The Cancer Genome Atlas for tumor/normal, cancer subtype, and mutation classification. Our CNNs are able to classify TCGA pathologist-annotated tumor/normal status of whole slide images (WSIs) in 19 cancer types with consistently high AUCs (0.995 ± 0.008), as well as subtypes with lower but significant accuracy (AUC 0.87 ± 0.1). Remarkably, tumor/normal CNNs trained on one tissue are effective in others (AUC 0.88 ± 0.11), with classifier relationships also recapitulating known adenocarcinoma, carcinoma, and developmental biology. Moreover, classifier comparisons reveal intra-slide spatial similarities, with an average tile-level correlation of 0.45 ± 0.16 between classifier pairs. Breast cancers, bladder cancers, and uterine cancers have spatial patterns that are particularly easy to detect, suggesting these cancers can be canonical types for image analysis. Patterns for TP53 mutations can also be detected, with WSI self- and cross-tissue AUCs ranging from 0.65-0.80. Finally, we comparatively evaluate CNNs on 170 breast and colon cancer images with pathologist-annotated nuclei, finding that both cellular and intercellular regions contribute to CNN accuracy. These results demonstrate the power of CNNs not only for histopathological classification, but also for cross-comparisons to reveal conserved spatial behaviors across tumors

Dynamics of the Ethanolamine Glycerophospholipid Remodeling Network

Peer reviewe

Deep learning-based cross-classifications reveal conserved spatial behaviors within tumor histological images

Histopathological images are a rich but incompletely explored data type for studying cancer. Manual inspection is time consuming, making it challenging to use for image data mining. Here we show that convolutional neural networks (CNNs) can be systematically applied across cancer types, enabling comparisons to reveal shared spatial behaviors. We develop CNN architectures to analyze 27,815 hematoxylin and eosin scanned images from The Cancer Genome Atlas for tumor/normal, cancer subtype, and mutation classification. Our CNNs are able to classify TCGA pathologist-annotated tumor/normal status of whole slide images (WSIs) in 19 cancer types with consistently high AUCs (0.995 ± 0.008), as well as subtypes with lower but significant accuracy (AUC 0.87 ± 0.1). Remarkably, tumor/normal CNNs trained on one tissue are effective in others (AUC 0.88 ± 0.11), with classifier relationships also recapitulating known adenocarcinoma, carcinoma, and developmental biology. Moreover, classifier comparisons reveal intra-slide spatial similarities, with an average tile-level correlation of 0.45 ± 0.16 between classifier pairs. Breast cancers, bladder cancers, and uterine cancers have spatial patterns that are particularly easy to detect, suggesting these cancers can be canonical types for image analysis. Patterns for TP53 mutations can also be detected, with WSI self- and cross-tissue AUCs ranging from 0.65-0.80. Finally, we comparatively evaluate CNNs on 170 breast and colon cancer images with pathologist-annotated nuclei, finding that both cellular and intercellular regions contribute to CNN accuracy. These results demonstrate the power of CNNs not only for histopathological classification, but also for cross-comparisons to reveal conserved spatial behaviors across tumors.R01 CA230031 - NCI NIH HHSPublished versio

Statistical Analysis of the Processes Controlling Choline and Ethanolamine Glycerophospholipid Molecular Species Composition

The regulation and maintenance of the cellular lipidome through biosynthetic, remodeling, and catabolic mechanisms are critical for biological homeostasis during development, health and disease. These complex mechanisms control the architectures of lipid molecular species, which have diverse yet highly regulated fatty acid chains at both the sn1 and sn2 positions. Phosphatidylcholine (PC) and phosphatidylethanolamine (PE) serve as the predominant biophysical scaffolds in membranes, acting as reservoirs for potent lipid signals and regulating numerous enzymatic processes. Here we report the first rigorous computational dissection of the mechanisms influencing PC and PE molecular architectures from high-throughput shotgun lipidomic data. Using novel statistical approaches, we have analyzed multidimensional mass spectrometry-based shotgun lipidomic data from developmental mouse heart and mature mouse heart, lung, brain, and liver tissues. We show that in PC and PE, sn1 and sn2 positions are largely independent, though for low abundance species regulatory processes may interact with both the sn1 and sn2 chain simultaneously, leading to cooperative effects. Chains with similar biochemical properties appear to be remodeled similarly. We also see that sn2 positions are more regulated than sn1, and that PC exhibits stronger cooperative effects than PE. A key aspect of our work is a novel statistically rigorous approach to determine cooperativity based on a modified Fisher's exact test using Markov Chain Monte Carlo sampling. This computational approach provides a novel tool for developing mechanistic insight into lipidomic regulation

A rising tide of parasite transcriptomics propels pathogen biology.

Twenty years ago, the first transcriptome of the intraerythrocytic developmental cycle of the malaria parasite Plasmodium falciparum was published in PLOS Biology. Since then, transcriptomics studies have transformed the study of parasite biology

Robust phenotype prediction from gene expression data using differential shrinkage of co-regulated genes

Abstract Discovery of robust diagnostic or prognostic biomarkers is a key to optimizing therapeutic benefit for select patient cohorts - an idea commonly referred to as precision medicine. Most discovery studies to derive such markers from high-dimensional transcriptomics datasets are weakly powered with sample sizes in the tens of patients. Therefore, highly regularized statistical approaches are essential to making generalizable predictions. At the same time, prior knowledge-driven approaches have been successfully applied to the manual interpretation of high-dimensional transcriptomics datasets. In this work, we assess the impact of combining two orthogonal approaches for the discovery of biomarker signatures, namely (1) well-known lasso-based regression approaches and its more recent derivative, the group lasso, and (2) the discovery of significant upstream regulators in literature-derived biological networks. Our method integrates both approaches in a weighted group-lasso model and differentially weights gene sets based on inferred active regulatory mechanism. Using nested cross-validation as well as independent clinical datasets, we demonstrate that our approach leads to increased accuracy and generalizable results. We implement our approach in a computationally efficient, user-friendly R package called creNET. The package can be downloaded at https://github.com/kouroshz/creNethttps://github.com/kouroshz/creNet and is accompanied by a parsed version of the STRING DB data base