New Algorithms for δγ-Order Preserving Matching

Context: Order-preserving matching regards the relative order of strings. However, its application areas require more flexibility in the matching paradigm. We advance in this direction in this paper that extends our previous work [27]. Method: We define γ -order preserving matching as an approximate variant of order-preserving matching. We devise two solutions for it based on segment and Fenwick trees: segtreeBA and bitBA. Results: We experimentally show the efficiency of our algorithms compared to the ones presented in [26] (naiveA and updateBA). Also, we present applications of our approach in music retrieval and stock market analysis. Conclusions: Even though the worst-case time complexity of the proposed algorithms (namely, O(nm log m)) is higher than the Ѳ(nm)-time complexity of updateBA, their Ω (n log n) lower bound makes them more efficient in practice. On the other hand, we show that our approach is useful to identify similarity in music melodies and stock price trends through real application examples

Nuevos Algoritmos para Búsqueda de Orden δγ

Context: Order-preserving matching regards the relative order of strings. However, its application areas require more flexibility in the matching paradigm. We advance in this direction in this paper that extends our previous work [27].Method: We define γ -order preserving matching as an approximate variant of order-preserving matching. We devise two solutions for it based on segment and Fenwick trees: segtreeBA and bitBA.Results: We experimentally show the efficiency of our algorithms compared to the ones presented in [26] (naiveA and updateBA). Also, we present applications of our approach in music retrieval and stock market analysis.Conclusions: Even though the worst-case time complexity of the proposed algorithms (namely, O(nm log m)) is higher than the Ѳ(nm)-time complexity of updateBA, their Ω (n log n) lower bound makes them more efficient in practice. On the other hand, we show that our approach is useful to identify similarity in music melodies and stock price trends through real application examples.Contexto: El emparejamiento de cadenas según el orden compara la estructura de las cadenas de texto. Sin embargo, sus áreas de aplicación requieren mayor flexibilidad en el criterio de comparación. Este artículo avanza en esta dirección al extender [27]. Método: Se define la búsqueda de orden – γ como una variante aproximada del problema de emparejamiento de cadenas según orden. Se proponen dos soluciones basadas en árboles de segmentos y árboles Fenwick: segtree BA and bit BA.Resultados: La eficiencia de los algoritmos propuestos se muestra experimentalmente comparándolos con los algoritmos presentados en [26] (naive A y update BA). Además, se presentan aplicaciones.Conclusiones: A pesar de que la complejidad en tiempo de peor-caso de los algoritmos propuestos (a decir, O (nm log m)) es mayor que la complejidad de update BA (Ѳ (nm)), su cota baja Ω(n log n) los hace más eficientes en la práctica. También se muestran aplicaciones del enfoque propuesto en recuperación de música y análisis del mercado de acciones con ejemplos reales

Model development and analysis techniques for epidemiological and neurobiological dynamics on networks

The interaction of entities on a network structure is of significant importance to many disciplines. Network structures can have both physical (e.g. power grids, computer networks, the World Wide Web, networks of neurones) and non-physical (e.g. social networks of friends, links between communities, the movement of livestock) realisations that are all amenable to study. In this thesis work on dynamical processes and the networks on which they occur is presented from a viewpoint of both mathematical epidemiology and computational/theoretical neuroscience, with additional consideration of the intersection between the two. I begin with a paper illustrating how different models of disease transmission are derivable from others and provide a framework for the development of approximate ODEs based on their derivation from exact Kolmogorov equations. This work is followed with two papers that use two such approximate models and consider how they perform when the interplay between both disease and network dynamics is taken into account. Whilst the work in these papers focusses on the modelling of the temporal evolution of the disease and network dynamics, papers four and five consider the recent viewpoint within neuroscience that the brain operates within a critical regime. Making use of models analogous to meanfield models in epidemiology I analyse the behaviour of the system when it is in a balanced state, characterised by the system operating at or near its critical bifurcation, and how this is relevant to the brain itself. Whilst models used within the two areas are analogous, the behavioural aspects of interest within them are quite different. I conclude with a discussion of these differences, the overlaps between both fields and suggest where future work in each area may benefit from incorporating methods and ideas of the other

Hierarchical dynamics of individual RNA helix base pair formation and disruption

This thesis explores the RNA folding problem using single-molecule field effect transistors (smFETs) to measure the lifetimes of individual RNA base-pairing rearrangements. In the course of this research, considerable computational, chemical, and engineering contributions were developed so that the single-molecule measurements could be conducted and quantified. These advancements have allowed, on the basis of the smFET data collected herein, the quantification of a kinetic model for RNA stem-loop structures which has been generalized to quantitatively explore the phenomenological observation that an RNA found in the bacillus subtilis strain acts as a metabolite-sensing switch, allowing RNA polymerase to transcribe the messenger RNA when the metabolite is present and preventing transcription when the metabolite is absent. Together, the data presented quantify a simple model for the base pairing rearrangements that underlie RNA folding

Rhythmogenesis and Bifurcation Analysis of 3-Node Neural Network Kernels

Central pattern generators (CPGs) are small neural circuits of coupled cells stably producing a range of multiphasic coordinated rhythmic activities like locomotion, heartbeat, and respiration. Rhythm generation resulting from synergistic interaction of CPG circuitry and intrinsic cellular properties remains deficiently understood and characterized. Pairing of experimental and computational studies has proven key in unlocking practical insights into operational and dynamical principles of CPGs, underlining growing consensus that the same fundamental circuitry may be shared by invertebrates and vertebrates. We explore the robustness of synchronized oscillatory patterns in small local networks, revealing universal principles of rhythmogenesis and multi-functionality in systems capable of facilitating stability in rhythm formation. Understanding principles leading to functional neural network behavior benefits future study of abnormal neurological diseases that result from perturbations of mechanisms governing normal rhythmic states. Qualitative and quantitative stability analysis of a family of reciprocally coupled neural circuits, constituted of generalized Fitzhugh–Nagumo neurons, explores symmetric and asymmetric connectivity within three-cell motifs, often forming constituent kernels within larger networks. Intrinsic mechanisms of synaptic release, escape, and post-inhibitory rebound lead to differing polyrhythmicity, where a single parameter or perturbation may trigger rhythm switching in otherwise robust networks. Bifurcation analysis and phase reduction methods elucidate qualitative changes in rhythm stability, permitting rapid identification and exploration of pivotal parameters describing biologically plausible network connectivity. Additional rhythm outcomes are elucidated, including phase-varying lags and broader cyclical behaviors, helping to characterize system capability and robustness reproducing experimentally observed outcomes. This work further develops a suite of visualization approaches and computational tools, describing robustness of network rhythmogenesis and disclosing principles for neuroscience applicable to other systems beyond motor-control. A framework for modular organization is introduced, using inhibitory and electrical synapses to couple well-characterized 3-node motifs described in this research as building blocks within larger networks to describe underlying cooperative mechanisms

The Network Science Of Distributed Representational Systems

From brains to science itself, distributed representational systems store and process information about the world. In brains, complex cognitive functions emerge from the collective activity of billions of neurons, and in science, new knowledge is discovered by building on previous discoveries. In both systems, many small individual units—neurons and scientific concepts—interact to inform complex behaviors in the systems they comprise. The patterns in the interactions between units are telling; pairwise interactions not only trivially affect pairs of units, but they also form structural and dynamic patterns with more than just pairs, on a larger scale of the network. Recently, network science adapted methods from graph theory, statistical mechanics, information theory, algebraic topology, and dynamical systems theory to study such complex systems. In this dissertation, we use such cutting-edge methods in network science to study complex distributed representational systems in two domains: cascading neural networks in the domain of neuroscience and concept networks in the domain of science of science. In the domain of neuroscience, the brain is a system that supports complex behavior by storing and processing information from the environment on long time scales. Underlying such behavior is a network of millions of interacting neurons. Many recent studies measure neural activity on the scale of the whole brain with brain regions as units or on the scale of brain regions with individual neurons as units. While many studies have explored the neural correlates of behaviors on these scales, it is less explored how neural activity can be decomposed into low-level patterns. Network science has shown potential to advance our understanding of large-scale brain networks, and here, we apply network science to further our understanding of low-level patterns in small-scale neural networks. Specifically, we explore how the structure and dynamics of biological neural networks support information storage and computation in spontaneous neural activity in slice recordings of rodent brains. Our results illustrate the relationships between network structure, dynamics, and information processing in neural systems. In the domain of science of science, the practice of science itself is a system that discovers and curates information about the physical and social world. For centuries, philosophers, historians, and sociologists of science have theorized about the process and practice of scientific discovery. Recently, the field of science of science has emerged to use a more data-driven approach to quantify the process of science. However, it remains unclear how recent advances in science of science either support or refute the various theories from the philosophies of science. Here, we use a network science approach to operationalize theories from prominent philosophers of science, and we test those theories using networks of hyperlinked articles in Wikipedia, the largest online encyclopedia. Our results support a nuanced view of philosophies of science—that science does not grow outward, as many may intuit, but by filling in gaps in knowledge. In this dissertation, we examine cascading neural networks first in Chapters 2 through 4 and then concept networks in Chapter 5. The studies in Chapters 2 to 4 highlight the role of patterns in the connections of neural networks in storing information and performing computations. The study in Chapter 5 describes patterns in the historical growth of concept networks of scientific knowledge from Wikipedia. Together, these analyses aim to shed light on the network science of distributed representational systems that store and process information about the world

Algebraic Topology for Data Scientists

This book gives a thorough introduction to topological data analysis (TDA), the application of algebraic topology to data science. Algebraic topology is traditionally a very specialized field of math, and most mathematicians have never been exposed to it, let alone data scientists, computer scientists, and analysts. I have three goals in writing this book. The first is to bring people up to speed who are missing a lot of the necessary background. I will describe the topics in point-set topology, abstract algebra, and homology theory needed for a good understanding of TDA. The second is to explain TDA and some current applications and techniques. Finally, I would like to answer some questions about more advanced topics such as cohomology, homotopy, obstruction theory, and Steenrod squares, and what they can tell us about data. It is hoped that readers will acquire the tools to start to think about these topics and where they might fit in.Comment: 322 pages, 69 figures, 5 table