3,273 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
Physically consistent simulation of transport of inertial particles in porous media
A new numerical approach is presented for simulating the movement of test particles suspended in an incompressible fluid flowing through a porous matrix. This two-phase particle-laden flow is based on the Navier-Stokes equations for incompressible fluid flow and equations of motion for the individual particles in which Stokes drag is dominant. The Immersed Boundary method is applied to incorporate the geometric complexity of the porous medium. A symmetry-preserving finite volume discretization method in combination with a volume penalization method resolves the flow within the porous material. The new Lagrangian particle tracking is such that for mass-less test particles no (numerical) collision with the coarsely represented porous medium occurs at any spatial resolution
Die Bestimmung des Physiologischen Aminosäurenstatus von Möhren und Weizen zur Unterscheidung ökol. und konv. Anbauvarianten
A procedure for the differentiation and identification of organic versus conventional grown crop is described. The validated (ISO 17025) procedure is based on the precise Determination of the N-Metabolom of the cultivated plant. With this procedure it was possible to distinguish organically from conventionally grown crops
Identifizierung von ökol. u. konv. Anbauvarianten bei DOK-Weizen mittels Fluoreszenz-Anregungs-Spektroskopie
At coded samples of wheat out of the DOK-trial of FiBL (Switzerland) it was possible to identify the organic and conventional grown variants. The method used was fluorescence-excitation-spectroscopy of whole samples. It was also possible to show differences between biodynamic and organic variants
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
Permanent Superhumps in V1974 Cyg
We present results of 32 nights of CCD photometry of V1974 Cygni, from the
years 1994 and 1995. We verify the presence of two distinct periodicities in
the light curve: 0.0812585 day~1.95 hours and 0.0849767 d~2.04 hr. We establish
that the shorter periodicity is the orbital period of the underlying binary
system. The longer period oscillates with an average value of |dot(P)| ~
3x10^(7)--typical to permanent superhumps. The two periods obey the linear
relation between the orbital and superhump periods that holds among members of
the SU Ursae Majoris class of dwarf novae. A third periodicity of 0.083204
d~2.00 hr appeared in 1994 but not in 1995. It may be related to the recently
discovered anti-superhump phenomenon. These results suggest a linkage between
the classical nova V1974 Cyg and the SU UMa stars, and indicate the existence
of an accretion disk and permanent superhumps in the system no later than 30
months after the nova outburst. From the precessing disk model of the superhump
phenomenon we estimate that the mass ratio in the binary system is between 2.2
and 3.6. Combined with previous results this implies a white dwarf mass of
0.75-1.07 M sun.Comment: 11 pages, 10 eps. figures, Latex, accepted for publication in MNRA
A quantitative central limit theorem for linear statistics of random matrix eigenvalues
It is known that the fluctuations of suitable linear statistics of Haar
distributed elements of the compact classical groups satisfy a central limit
theorem. We show that if the corresponding test functions are sufficiently
smooth, a rate of convergence of order almost can be obtained using a
quantitative multivariate CLT for traces of powers that was recently proven
using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions;
accepted for publication in the Journal of Theoretical Probabilit
- …