Browsing by Subject "Time series analysis"

This work introduces geometric and topological data analysis (TDA) tools that can be used in conjunction with sliding window transformations, also known as delay-embeddings, for discovering structure in time series and dynamical systems in an unsupervised or supervised learning framework. For signals of unknown period, we introduce an intuitive topological method to discover the period, and we demonstrate its use in synthetic examples and real temperature data. Alternatively, for almost-periodic signals of known period, we introduce a metric called Geometric Complexity of an Almost Periodic signal (GCAP), based on a topological construction, which allows us to continuously measure the evolving variation of its periods. We apply this method to temperature data collected from over 200 weather stations in the United States and describe the novel patterns that we observe. Next, we show how geometric and TDA tools can be used in a supervised learning framework. Seizure-detection using electroencephalogram (EEG) data is formulated as a binary classification problem. We define new collections of geometric and topological features of multi-channel data, which utilizes temporal and spatial context of EEG, and show how it results in better overall performance of seizure detection than using the usual time-domain and frequency domain features. Finally, we introduce a novel method to sonify persistence diagrams, and more generally any planar point cloud, using a modified version of the harmonic table. This auditory display can be useful for finding patterns that visual analysis alone may miss.

DNA, the blueprint of life, is more than a carrier of genetic information. It offers a highly programmable substrate that can be used for computing, nanorobotics, and advanced imaging techniques. In this work, we use the programmable nature of synthetic DNA to engineer two novel applications. In the first part, DNA is programmed to improve the multiplexing capabilities of a fluorescence microscope while in the second part, we design a novel DNA computing architecture that uses a strand displacing polymerase enzyme. This thesis is a collection of 2 experimental papers, 2 theory papers, and 1 software paper. The general theme of this thesis is to exploit the programmable nature of DNA to develop new applications for the wider field of molecular biology, nanoimaging, and computer engineering.

Optical multiplexing is defined as the ability to study, detect, or quantify multiple objects of interest simultaneously. There are several ways to improve optical multiplexing, namely, using orthogonal wavelengths, multiple mesoscale geometries, orthogonal nucleic acid probes, or a combination of these. Most traditional techniques employ either the geometry or the color of single molecules to uniquely identify (or barcode) different species of interest. However, these techniques require complex sample preparation and multicolor hardware setup. In this work, we introduce a time-based amplification-free single-molecule barcoding technique using easy-to-design nucleic acid strands. A dye-labeled complementary reporter strand transiently binds to the programmed nucleic acid strands to emit temporal intensity signals. We program the DNA strands to emit uniquely identifiable temporal signals for molecular-scale fingerprinting. Since the reporters bind transiently to DNA devices, our method offers relative immunity to photobleaching. We use a single universal reporter strand for all DNA devices making our design extremely cost-effective. We show DNA strands can be programmed for generating a multitude of uniquely identifiable molecular barcodes. Our technique can be easily incorporated with the existing orthogonal methods that use wavelength or geometry to generate a large pool of distinguishable molecular barcodes thereby enhancing the overall multiplexing capabilities of single-molecule imaging. The proposed project has exciting transformative potential for nanoscale applications in fluorescence microscopy and cell biology since the development of temporal barcodes would allow for applications such as sensing miRNAs which are largely associated with disease diagnosis and therapeutics.

The regulation of cellular and molecular processes typically involves complex biochemical networks. Synthetic nucleic acid reaction networks (both enzyme-based and enzyme-free) can be systematically designed to approximate sophisticated biochemical processes. However, most of the prior experimental protocols for chemical reaction networks (CRNs) relied on either strand-displacement hybridization or restriction and exonuclease enzymatic reactions. These resulting synthetic systems usually suffer from either slow rates or leaky reactions. This work proposes an alternative architecture to implement arbitrary reaction networks, that is based entirely on strand-displacing polymerase reactions with nonoverlapping I/O sequences. First, the design for a simple protocol that can approximate arbitrary unimolecular and bimolecular reactions using polymerase strand displacement reactions is presented. Then these fundamental reaction systems are used as modules to show large-scale applications of the architecture, including an autocatalytic amplifier, a molecular-scale consensus protocol, and a dynamic oscillatory system. Finally, we engineer an \textit{in vitro} catalytic amplifier system as a proof-of-concept of our polymerase architecture since such sustainable amplifiers require careful sequence design and implementation.

Today, large-scale scientific applications are both data driven and distributed. To support the scale and inherent distribution of these applications, significant heterogeneous and geographically distributed resources are required over long periods of time to ensure adequate performance. Furthermore, the behavior of these applications depends on a large number of factors related to the application, the system software, the underlying hardware, and other running applications, as well as potential interactions among these factors.

Most Grid application users are primarily concerned with obtaining the result of the application as fast as possible, without worrying about the details involved in monitoring and understanding factors affecting application performance. In this work, we aim to provide the application users with a simple and intuitive performance evaluation mechanism during the execution time of their long-running Grid applications or workflows. Our performance evaluation mechanism provides a qualitative and periodic assessment of the application's behavior by informing the user whether the application's performance is expected or unexpected. Furthermore, it can help improve overall application performance by informing and guiding fault-tolerance services when the application exhibits persistent unexpected performance behaviors.

This thesis addresses the hypotheses that in order to qualitatively assess application behavioral states in long-running scientific Grid applications: (1) it is necessary to extract temporal information in performance time series data, and that (2) it is sufficient to extract variance and pattern as specific examples of temporal information. Evidence supporting these hypotheses can lead to the ability to qualitatively assess the overall behavior of the application and, if needed, to offer a most likely diagnostic of the underlying problem.

To test the stated hypotheses, we develop and evaluate a general qualitative performance analysis framework that incorporates (a) techniques from time series analysis and machine learning to extract and learn from data, structural and temporal features associated with application performance in order to reach a qualitative interpretation of the application's behavior, and (b) mechanisms and policies to reason over time and across the distributed resource space about the behavior of the application.

Experiments with two scientific applications from meteorology and astronomy comparing signatures generated from instantaneous values of performance data versus those generated from temporal characteristics support the former hypothesis that temporal information is necessary to extract from performance time series data to be able to accurately interpret the behavior of these applications. Furthermore, temporal signatures incorporating variance and pattern information generated for these applications reveal signatures that have distinct characteristics during well-performing versus poor-performing executions. This leads to the framework's accurate classification of instances of similar behaviors, which represents supporting evidence for the latter hypothesis. The proposed framework's ability to generate a qualitative assessment of performance behavior for scientific applications using temporal information present in performance time series data represents a step towards simplifying and improving the quality of service for Grid applications.