93 research outputs found
Weighted Frechet Means as Convex Combinations in Metric Spaces: Properties and Generalized Median Inequalities
In this short note, we study the properties of the weighted Frechet mean as a
convex combination operator on an arbitrary metric space, (Y,d). We show that
this binary operator is commutative, non-associative, idempotent, invariant to
multiplication by a constant weight and possesses an identity element. We also
treat the properties of the weighted cumulative Frechet mean. These tools allow
us to derive several types of median inequalities for abstract metric spaces
that hold for both negative and positive Alexandrov spaces. In particular, we
show through an example that these bounds cannot be improved upon in general
metric spaces. For weighted Frechet means, however, such inequalities can
solely be derived for weights equal or greater than one. This latter limitation
highlights the inherent difficulties associated with working with
abstract-valued random variables.Comment: 7 pages, 1 figure. Submitted to Probability and Statistics Letter
Evidence for GeV emission from the Galactic Center Fountain
The region near the Galactic center may have experienced recurrent episodes
of injection of energy in excess of 10 ergs due to repeated
starbursts involving more than 10 supernovae. This hypothesis can be
tested by measurements of -ray lines produced by the decay of
radioactive isotopes and positron annihilation, or by searches for pulsars
produced during starbursts. Recent OSSE observations of 511 keV emission
extending above the Galactic center led to the suggestion of a starburst driven
fountain from the Galactic center. We present EGRET observations that might
support this picture.Comment: 5 pages, 1 embedded Postscript figure. To appear in the Proceedings
of the Fourth Compton Symposiu
Improvement of experimental testing and network training conditions with genome-wide microarrays for more accurate predictions of drug gene targets
BACKGROUND: Genome-wide microarrays have been useful for predicting chemical-genetic interactions at the gene level. However, interpreting genome-wide microarray results can be overwhelming due to the vast output of gene expression data combined with off-target transcriptional responses many times induced by a drug treatment. This study demonstrates how experimental and computational methods can interact with each other, to arrive at more accurate predictions of drug-induced perturbations. We present a two-stage strategy that links microarray experimental testing and network training conditions to predict gene perturbations for a drug with a known mechanism of action in a well-studied organism. RESULTS: S. cerevisiae cells were treated with the antifungal, fluconazole, and expression profiling was conducted under different biological conditions using Affymetrix genome-wide microarrays. Transcripts were filtered with a formal network-based method, sparse simultaneous equation models and Lasso regression (SSEM-Lasso), under different network training conditions. Gene expression results were evaluated using both gene set and single gene target analyses, and the drug’s transcriptional effects were narrowed first by pathway and then by individual genes. Variables included: (i) Testing conditions – exposure time and concentration and (ii) Network training conditions – training compendium modifications. Two analyses of SSEM-Lasso output – gene set and single gene – were conducted to gain a better understanding of how SSEM-Lasso predicts perturbation targets. CONCLUSIONS: This study demonstrates that genome-wide microarrays can be optimized using a two-stage strategy for a more in-depth understanding of how a cell manifests biological reactions to a drug treatment at the transcription level. Additionally, a more detailed understanding of how the statistical model, SSEM-Lasso, propagates perturbations through a network of gene regulatory interactions is achieved.Published versio
Hypothesis Testing For Network Data in Functional Neuroimaging
In recent years, it has become common practice in neuroscience to use
networks to summarize relational information in a set of measurements,
typically assumed to be reflective of either functional or structural
relationships between regions of interest in the brain. One of the most basic
tasks of interest in the analysis of such data is the testing of hypotheses, in
answer to questions such as "Is there a difference between the networks of
these two groups of subjects?" In the classical setting, where the unit of
interest is a scalar or a vector, such questions are answered through the use
of familiar two-sample testing strategies. Networks, however, are not Euclidean
objects, and hence classical methods do not directly apply. We address this
challenge by drawing on concepts and techniques from geometry, and
high-dimensional statistical inference. Our work is based on a precise
geometric characterization of the space of graph Laplacian matrices and a
nonparametric notion of averaging due to Fr\'echet. We motivate and illustrate
our resulting methodologies for testing in the context of networks derived from
functional neuroimaging data on human subjects from the 1000 Functional
Connectomes Project. In particular, we show that this global test is more
statistical powerful, than a mass-univariate approach. In addition, we have
also provided a method for visualizing the individual contribution of each edge
to the overall test statistic.Comment: 34 pages. 5 figure
Evidence for a Galactic gamma ray halo
We present quantitative statistical evidence for a -ray emission halo
surrounding the Galaxy. Maps of the emission are derived. EGRET data were
analyzed in a wavelet-based non-parametric hypothesis testing framework, using
a model of expected diffuse (Galactic + isotropic) emission as a null
hypothesis. The results show a statistically significant large scale halo
surrounding the center of the Milky Way as seen from Earth. The halo flux at
high latitudes is somewhat smaller than the isotropic gamma-ray flux at the
same energy, though of the same order (O(10^(-7)--10^(-6)) ph/cm^2/s/sr above 1
GeV).Comment: Final version accepted for publication in New Astronomy. Some
additional results/discussion included, along with entirely revised figures.
19 pages, 15 figures, AASTeX. Better quality figs (PS and JPEG) are available
at http://tigre.ucr.edu/halo/paper.htm
Bayesian Blocks, A New Method to Analyze Structure in Photon Counting Data
I describe a new time-domain algorithm for detecting localized structures
(bursts), revealing pulse shapes, and generally characterizing intensity
variations. The input is raw counting data, in any of three forms: time-tagged
photon events (TTE), binned counts, or time-to-spill (TTS) data. The output is
the most likely segmentation of the observation into time intervals during
which the photon arrival rate is perceptibly constant -- i.e. has a fixed
intensity without statistically significant variations. Since the analysis is
based on Bayesian statistics, I call the resulting structures Bayesian Blocks.
Unlike most, this method does not stipulate time bins -- instead the data
themselves determine a piecewise constant representation. Therefore the
analysis procedure itself does not impose a lower limit to the time scale on
which variability can be detected. Locations, amplitudes, and rise and decay
times of pulses within a time series can be estimated, independent of any
pulse-shape model -- but only if they do not overlap too much, as deconvolution
is not incorporated. The Bayesian Blocks method is demonstrated by analyzing
pulse structure in BATSE -ray data. The MatLab scripts and sample data
can be found on the WWW at: http://george.arc.nasa.gov/~scargle/papers.htmlComment: 42 pages, 2 figures; revision correcting mathematical errors;
clarifications; removed Cyg X-1 sectio
Network inference - with confidence - from multivariate time series
Networks - collections of interacting elements or nodes - abound in the
natural and manmade worlds. For many networks, complex spatiotemporal dynamics
stem from patterns of physical interactions unknown to us. To infer these
interactions, it is common to include edges between those nodes whose time
series exhibit sufficient functional connectivity, typically defined as a
measure of coupling exceeding a pre-determined threshold. However, when
uncertainty exists in the original network measurements, uncertainty in the
inferred network is likely, and hence a statistical propagation-of-error is
needed. In this manuscript, we describe a principled and systematic procedure
for the inference of functional connectivity networks from multivariate time
series data. Our procedure yields as output both the inferred network and a
quantification of uncertainty of the most fundamental interest: uncertainty in
the number of edges. To illustrate this approach, we apply our procedure to
simulated data and electrocorticogram data recorded from a human subject during
an epileptic seizure. We demonstrate that the procedure is accurate and robust
in both the determination of edges and the reporting of uncertainty associated
with that determination.Comment: 12 pages, 7 figures (low resolution), submitte
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