1,587 research outputs found

    Wolf Man, Part II

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    Network Theory Approaches for the Analysis of Ordered Data.

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    PhD ThesisGraphs are mathematical structures comprised of a set of nodes connected by edges, and network science is the application of graph theory to real world data. Networks are used as a model to analyse how entities, either individual actors, or complex systems, interact with one another. The research here will consist of extracting networks (we will use the terms \graph" and \network" interchangeably) from ordered series, which we will focus on series ordered by time. We will either do this with the aid of the visibility graph, which is a method, based on visibility, for mapping a time series in to a graph, or through estimating the wavelet correlation, a more conventional method used in neuroscience. The aim is to describe the structure of time series and their underlying dynamical properties in graphtheoretical terms, and then using this motivation to analyse large data sets spanning several disciplines. We will describe a method, using the visibility graph, for quantifying reversibility of non-stationary processes and apply this method to a large nancial data set, with the intent of ranking companies based on their irreversibility. We also use the visibility graph to develop a method which e ciently quanti es the asymmetries between minima and maxima in time series, and we then apply the method to a variety of data sets. Continuing with the theme of visibility, we study the spectral properties of visibility graphs extracted from trajectories of the logistic map undergoing a period-doubling route to chaos (known as the Feigenbaum scenario). Finally, we will use wavelet correlation to construct networks from fMRI time series, and examine community structure with the aim of di erentiating between brain networks of patients with schizophrenia from control subjects. The general format throughout this thesis will start with theory, followed by extensive numerical simulations, which we can then apply the methods to real data sets

    SYSTEM, METHOD, AND COMPUTER PROGRAM PRODUCT FOR AUTOMATICALLY SCRAPING CATEGORICAL DATA FROM A PLURALITY OF WEBSITES

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    Systems, methods, and computer program products are provided for automatically scraping categorical data from a plurality of websites. These include: determining a product category; identifying a first website including data associated with the product category; automatically scraping the first website to compile first product data associated with the product category; generating a plurality of web queries based on the compiled first product data; executing the plurality of web queries to identify a plurality of websites; automatically scraping at least a portion of the plurality of websites to compile supplier data associated with suppliers in the product category; and storing at least a portion of the compiled supplier data in a database

    Time reversibility from visibility graphs of nonstationary processes

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    Visibility algorithms are a family of methods to map time series into networks, with the aim of describing the structure of time series and their underlying dynamical properties in graph-theoretical terms. Here we explore some properties of both natural and horizontal visibility graphs associated to several non-stationary processes, and we pay particular attention to their capacity to assess time irreversibility. Non-stationary signals are (infinitely) irreversible by definition (independently of whether the process is Markovian or producing entropy at a positive rate), and thus the link between entropy production and time series irreversibility has only been explored in non-equilibrium stationary states. Here we show that the visibility formalism naturally induces a new working definition of time irreversibility, which allows to quantify several degrees of irreversibility for stationary and non-stationary series, yielding finite values that can be used to efficiently assess the presence of memory and off-equilibrium dynamics in non-stationary processes without needs to differentiate or detrend them. We provide rigorous results complemented by extensive numerical simulations on several classes of stochastic processes

    Dependence on Over the Counter (OTC) Codeine Containing Analgesics: Treatment and Recovery with Buprenorphine Naloxone

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    Misuse and dependence on prescribed and over the counter (OTC) codeine-combination analgesics is an emerging public health concern. We present a clinical case series of four adult patients dependent on OTC codeine combination analgesics in Ireland. Cases (two males/two females, aged 44–57 years) were consuming between 12 and 72 codeine-containing tablets/day. In three cases, consumption was linked to pain, with on-going misuse reflecting dependence on codeine. Cases were initiated on buprenorphine-naloxone (Suboxone®), stabilised on doses of between 4 mg/1 mg and 14 mg/3.5 mg per day and remain on treatment without additional opioid use, as verified by drug screening reports. Although anecdotal, these cases show the potential of effective opioid assisted treatment (OAT) using buprenorphine-naloxone (Suboxone®) to successfully treat this distinct form of opioid dependence disorder. Optimal service provision should recognise unique patient profiles and needs for this form of opioid dependence and incorporate psycho-social supports

    On the spectral properties of Feigenbaum graphs

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    A Horizontal Visibility Graph (HVG) is a simple graph extracted from an ordered sequence of real values, and this mapping has been used to provide a combinatorial encryption of time series for the task of performing network based time series analysis. While some properties of the spectrum of these graphs --such as the largest eigenvalue of the adjacency matrix-- have been routinely used as measures to characterise time series complexity, a theoretic understanding of such properties is lacking. In this work we explore some algebraic and spectral properties of these graphs associated to periodic and chaotic time series. We focus on the family of Feigenbaum graphs, which are HVGs constructed in correspondence with the trajectories of one-parameter unimodal maps undergoing a period-doubling route to chaos (Feigenbaum scenario). For the set of values of the map's parameter μ\mu for which the orbits are periodic with period 2n2^n, Feigenbaum graphs are fully characterised by two integers (n,k) and admit an algebraic structure. We explore the spectral properties of these graphs for finite n and k, and among other interesting patterns we find a scaling relation for the maximal eigenvalue and we prove some bounds explaining it. We also provide numerical and rigorous results on a few other properties including the determinant or the number of spanning trees. In a second step, we explore the set of Feigenbaum graphs obtained for the range of values of the map's parameter μ\mu for which the system displays chaos. We show that in this case, Feigenbaum graphs form an ensemble for each value of μ\mu and the system is typically weakly self-averaging. Unexpectedly, we find that while the largest eigenvalue can distinguish chaos from an iid process, it is not a good measure to quantify the chaoticity of the process, and that the eigenvalue density does a better job.Comment: 33 page

    Evolution of circular, non-equatorial orbits of Kerr black holes due to gravitational-wave emission: II. Inspiral trajectories and gravitational waveforms

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    The inspiral of a ``small'' (μ∼1−100M⊙\mu \sim 1-100 M_\odot) compact body into a ``large'' (M∼105−7M⊙M \sim 10^{5-7} M_\odot) black hole is a key source of gravitational radiation for the space-based gravitational-wave observatory LISA. The waves from such inspirals will probe the extreme strong-field nature of the Kerr metric. In this paper, I investigate the properties of a restricted family of such inspirals (the inspiral of circular, inclined orbits) with an eye toward understanding observable properties of the gravitational waves that they generate. Using results previously presented to calculate the effects of radiation reaction, I assemble the inspiral trajectories (assuming that radiation reacts adiabatically, so that over short timescales the trajectory is approximately geodesic) and calculate the wave generated as the compact body spirals in. I do this analysis for several black hole spins, sampling a range that should be indicative of what spins we will encounter in nature. The spin has a very strong impact on the waveform. In particular, when the hole rotates very rapidly, tidal coupling between the inspiraling body and the event horizon has a very strong influence on the inspiral time scale, which in turn has a big impact on the gravitational wave phasing. The gravitational waves themselves are very usefully described as ``multi-voice chirps'': the wave is a sum of ``voices'', each corresponding to a different harmonic of the fundamental orbital frequencies. Each voice has a rather simple phase evolution. Searching for extreme mass ratio inspirals voice-by-voice may be more effective than searching for the summed waveform all at once.Comment: 15 pages, 11 figures, accepted for publication in PRD. This version incorporates referee's comments, and is much less verbos
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