2,546 research outputs found
Model-Twin Randomization (MoTR): A Monte Carlo Method for Estimating the Within-Individual Average Treatment Effect Using Wearable Sensors
Temporally dense single-person "small data" have become widely available
thanks to mobile apps and wearable sensors. Many caregivers and self-trackers
want to use these data to help a specific person change their behavior to
achieve desired health outcomes. Ideally, this involves discerning possible
causes from correlations using that person's own observational time series
data. In this paper, we estimate within-individual average treatment effects of
physical activity on sleep duration, and vice-versa. We introduce the model
twin randomization (MoTR; "motor") method for analyzing an individual's
intensive longitudinal data. Formally, MoTR is an application of the g-formula
(i.e., standardization, back-door adjustment) under serial interference. It
estimates stable recurring effects, as is done in n-of-1 trials and single case
experimental designs. We compare our approach to standard methods (with
possible confounding) to show how to use causal inference to make better
personalized recommendations for health behavior change, and analyze 222 days
of Fitbit sleep and steps data for one of the authors.Comment: 27 pages, 2 figures, 5 tables; appendix include
Warming of the Antarctic ice-sheet surface since the 1957 International Geophysical Year
Assessments of Antarctic temperature change have emphasized the contrast between strong warming of the Antarctic Peninsula and slight cooling of the Antarctic continental interior in recent decades. This pattern of temperature change has been attributed to the increased strength of the circumpolar westerlies, largely in response to changes in stratospheric ozone. This picture, however, is substantially incomplete owing to the sparseness and short duration of the observations. Here we show that significant warming extends well beyond the Antarctic Peninsula to cover most of West Antarctica, an area of warming much larger than previously reported. West Antarctic warming exceeds 0.1 °C per decade over the past 50 years, and is strongest in winter and spring. Although this is partly offset by autumn cooling in East Antarctica, the continent-wide average near-surface temperature trend is positive. Simulations using a general circulation model reproduce the essential features of the spatial pattern and the long-term trend, and we suggest that neither can be attributed directly to increases in the strength of the westerlies. Instead, regional changes in atmospheric circulation and associated changes in sea surface temperature and sea ice are required to explain the enhanced warming in West Antarctica
Imaging a Quasar Accretion Disk with Microlensing
We show how analysis of a quasar high-magnification microlensing event may be
used to construct a map of the frequency-dependent surface brightness of the
quasar accretion disk. The same procedure also allows determination of the disk
inclination angle, the black hole mass (modulo the caustic velocity), and
possibly the black hole spin. This method depends on the validity of one
assumption: that the optical and ultraviolet continuum of the quasar is
produced on the surface of an azimuthally symmetric, flat equatorial disk,
whose gas follows prograde circular orbits in a Kerr spacetime (and plunges
inside the marginally stable orbit). Given this assumption, we advocate using a
variant of first-order linear regularization to invert multi-frequency
microlensing lightcurves to obtain the disk surface brightness as a function of
radius and frequency. The other parameters can be found by minimizing
chi-square in a fashion consistent with the regularized solution for the
surface brightness.
We present simulations for a disk model appropriate to the Einstein Cross
quasar, an object uniquely well-suited to this approach. These simulations
confirm that the surface brightness can be reconstructed quite well near its
peak, and that there are no systematic errors in determining the other model
parameters. We also discuss the observational requirements for successful
implementation of this technique.Comment: accepted to ApJ for publicatio
Extensions of tempered representations
Let be irreducible tempered representations of an affine Hecke
algebra H with positive parameters. We compute the higher extension groups
explicitly in terms of the representations of analytic
R-groups corresponding to and . The result has immediate
applications to the computation of the Euler-Poincar\'e pairing ,
the alternating sum of the dimensions of the Ext-groups. The resulting formula
for is equal to Arthur's formula for the elliptic pairing of
tempered characters in the setting of reductive p-adic groups. Our proof
applies equally well to affine Hecke algebras and to reductive groups over
non-archimedean local fields of arbitrary characteristic. This sheds new light
on the formula of Arthur and gives a new proof of Kazhdan's orthogonality
conjecture for the Euler-Poincar\'e pairing of admissible characters.Comment: This paper grew out of "A formula of Arthur and affine Hecke
algebras" (arXiv:1011.0679). In the second version some minor points were
improve
- …