17,107 research outputs found
Persistent homology of time-dependent functional networks constructed from coupled time series
We use topological data analysis to study "functional networks" that we
construct from time-series data from both experimental and synthetic sources.
We use persistent homology with a weight rank clique filtration to gain
insights into these functional networks, and we use persistence landscapes to
interpret our results. Our first example uses time-series output from networks
of coupled Kuramoto oscillators. Our second example consists of biological data
in the form of functional magnetic resonance imaging (fMRI) data that was
acquired from human subjects during a simple motor-learning task in which
subjects were monitored on three days in a five-day period. With these
examples, we demonstrate that (1) using persistent homology to study functional
networks provides fascinating insights into their properties and (2) the
position of the features in a filtration can sometimes play a more vital role
than persistence in the interpretation of topological features, even though
conventionally the latter is used to distinguish between signal and noise. We
find that persistent homology can detect differences in synchronization
patterns in our data sets over time, giving insight both on changes in
community structure in the networks and on increased synchronization between
brain regions that form loops in a functional network during motor learning.
For the motor-learning data, persistence landscapes also reveal that on average
the majority of changes in the network loops take place on the second of the
three days of the learning process.Comment: 17 pages (+3 pages in Supplementary Information), 11 figures in many
text (many with multiple parts) + others in SI, submitte
Silicon and magnesium in planetary nebulae
The IUE satellite spectra of some planetary nebulae show features due to silicon and magnesium: Si III wavelengths 1883, 1892; Si IV wavelengths 1394, 1403; Mg II wavelengths 2796, 2804 and Mg V wavelengths 2784, 2929. With the aid of modeling techniques, the corresponding elemental abundances are found. In addition to previous observations of NGC 7662 and IC 418, data were found for NGC 2440, Hu 1-2, IC 2003 and IC 2165. Silicon appears depleted by up to an order of magnitude relative to the sun. Large variations of magnesium abundance are found, which are likely to reflect differing degrees of depletion due to grain formation
Elemental abundances in high-excitation planetary nebulae
The IUE satellite was used to obtain low dispersion spectra of the high excitation planetary nebulae IC 351, IC 2003, NGC 2022, IC 2165, NGC 2440, Hu 1-2, and IC 5217. Numerical modeling was undertaken to determine the chemical composition of these objects with particular emphasis on obtaining elemental carbon and nitrogen abundances. Large variations in the C/N ratio from object to object are suggested
Thrust performance of isolated 36-chute suppressor plug nozzles with and without ejectors at Mach numbers from 0 to 0.45
Plug nozzles with chute-type noise suppressors were tested with and without ejector shrouds at free-stream Mach numbers from 0 to 0.45 and over a range of nozzle pressure ratios from 2 to 4. A 36-chute suppressor nozzle with an ejector had an efficiency of 94.6 percent at an assumed takeoff pressure ratio of 3.0 and a Mach number of 0.36. This represents only a 3.4 percent performance penalty when compared with the 98 percent efficiency obtained with a previously tested unsuppressed plug nozzle
Thrust performance of isolated, two-dimensional suppressed plug nozzles with and without ejectors at Mach numbers from 0 to 0.45
A series of two-dimensional plug nozzles was tested with and without ejector shrouds at free stream Mach numbers from 0 to 0.45 and over a range of nozzle pressure ratios from 2 to 4. These nozzles were also tested with and without chute noise suppressors. A two-dimensional plug nozzle has an efficiency of 96.1 percent at an assumed takeoff pressure ratio of 3.0 and Mach 0.36. A 12-chute suppressed nozzle with sidewalls has an efficiency of 81.0 percent (15.1 percent below the unsuppressed nozzle)
Topological Data Analysis of Task-Based fMRI Data from Experiments on Schizophrenia
We use methods from computational algebraic topology to study functional
brain networks, in which nodes represent brain regions and weighted edges
encode the similarity of fMRI time series from each region. With these tools,
which allow one to characterize topological invariants such as loops in
high-dimensional data, we are able to gain understanding into low-dimensional
structures in networks in a way that complements traditional approaches that
are based on pairwise interactions. In the present paper, we use persistent
homology to analyze networks that we construct from task-based fMRI data from
schizophrenia patients, healthy controls, and healthy siblings of schizophrenia
patients. We thereby explore the persistence of topological structures such as
loops at different scales in these networks. We use persistence landscapes and
persistence images to create output summaries from our persistent-homology
calculations, and we study the persistence landscapes and images using
-means clustering and community detection. Based on our analysis of
persistence landscapes, we find that the members of the sibling cohort have
topological features (specifically, their 1-dimensional loops) that are
distinct from the other two cohorts. From the persistence images, we are able
to distinguish all three subject groups and to determine the brain regions in
the loops (with four or more edges) that allow us to make these distinctions
Monte Carlo Simulation of Lyman Alpha Scattering and Application to Damped Lyman Alpha Systems
A Monte Carlo code to solve the transfer of Lyman alpha (Lya) photons is
developed, which can predict the Lya image and two-dimensional Lya spectra of a
hydrogen cloud with any given geometry, Lya emissivity, neutral hydrogen
density distribution, and bulk velocity field. We apply the code to several
simple cases of a uniform cloud to show how the Lya image and emitted line
spectrum are affected by the column density, internal velocity gradients, and
emissivity distribution. We then apply the code to two models for damped Lya
absorption systems: a spherical, static, isothermal cloud, and a flattened,
axially symmetric, rotating cloud. If the emission is due to fluorescence of
the external background radiation, the Lya image should have a core
corresponding to the region where hydrogen is self-shielded. The emission line
profile has the characteristic double peak with a deep central trough. We show
how rotation of the cloud causes the two peaks to shift in wavelength as the
slit is perpendicular to the rotation axis, and how the relative amplitude of
the two peaks is changed. In reality, damped Lya systems are likely to have a
clumpy gas distribution with turbulent velocity fields, which should smooth the
line emission profile, but should still leave the rotation signature of the
wavelength shift across the system.Comment: 19 pages, 17 eps figures. One panel is added in Fig.1 to show the
recoil effect. Revisions are made in response to the referee's comments.
Accepted for publication in Ap
Numerical algebraic geometry for model selection and its application to the life sciences
Researchers working with mathematical models are often confronted by the
related problems of parameter estimation, model validation, and model
selection. These are all optimization problems, well-known to be challenging
due to non-linearity, non-convexity and multiple local optima. Furthermore, the
challenges are compounded when only partial data is available. Here, we
consider polynomial models (e.g., mass-action chemical reaction networks at
steady state) and describe a framework for their analysis based on optimization
using numerical algebraic geometry. Specifically, we use probability-one
polynomial homotopy continuation methods to compute all critical points of the
objective function, then filter to recover the global optima. Our approach
exploits the geometric structures relating models and data, and we demonstrate
its utility on examples from cell signaling, synthetic biology, and
epidemiology.Comment: References added, additional clarification
Topological data analysis of contagion maps for examining spreading processes on networks
Social and biological contagions are influenced by the spatial embeddedness
of networks. Historically, many epidemics spread as a wave across part of the
Earth's surface; however, in modern contagions long-range edges -- for example,
due to airline transportation or communication media -- allow clusters of a
contagion to appear in distant locations. Here we study the spread of
contagions on networks through a methodology grounded in topological data
analysis and nonlinear dimension reduction. We construct "contagion maps" that
use multiple contagions on a network to map the nodes as a point cloud. By
analyzing the topology, geometry, and dimensionality of manifold structure in
such point clouds, we reveal insights to aid in the modeling, forecast, and
control of spreading processes. Our approach highlights contagion maps also as
a viable tool for inferring low-dimensional structure in networks.Comment: Main Text and Supplementary Informatio
The development and evaluation of exercises for group response to word meaning for increasing the speed of word recognition in grade I
Thesis (Ed.M.)--Boston Universit
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