33,377 research outputs found
Navigation in Curved Space-Time
A covariant and invariant theory of navigation in curved space-time with
respect to electromagnetic beacons is written in terms of J. L. Synge's
two-point invariant world function. Explicit equations are given for navigation
in space-time in the vicinity of the Earth in Schwarzschild coordinates and in
rotating coordinates. The restricted problem of determining an observer's
coordinate time when their spatial position is known is also considered
Constraints on gravity: An evidence against the covariant resolution of the Pioneer anomaly
We consider corrections in the form of to the
Einstein-Hilbert Lagrangian. Then we compute the corrections to the
Schwarszchild geometry due to the inclusion of this general term to the
Lagrangian. We show that
gives rise to a constant anomalous acceleration for objects orbiting the Sun
onward the Sun. This leads to the conclusion that would have covariantly
resolved the Pioneer anomaly if this value of had not
contradicted other observations.
We notice that the experimental bounds on grows stronger in case
we examine the deformation of the space-time geometry around objects lighter
than the Sun. We therefore use the high precision measurements around the Earth
(LAGEOS and LLR) and obtain a very strong constraint on the corrections in the
form of and in particular . This bound requires
.
Therefore it refutes the covariant resolution of the Pioneer anomaly.Comment: ...v5: references added, new discussions adde
Error correction for deep space network teletype circuits
Error detection codes and correction devices for Deep Space Network /DSN/ teletypewriter system
A new perspective on Einstein's philosophy of cosmology
The recent discovery that Einstein once attempted - and quickly abandoned - a
steady-state model of the expanding universe sheds new light on his
philosophical journey from static to dynamic cosmologies.Comment: Revised book chapter. To be published in 'The Philosophy of
Cosmology:Foundations and Perspectives'. Eds J.Silk and J.Barrow (Cambridge
University Press
Exact heat kernel on a hypersphere and its applications in kernel SVM
Many contemporary statistical learning methods assume a Euclidean feature
space. This paper presents a method for defining similarity based on
hyperspherical geometry and shows that it often improves the performance of
support vector machine compared to other competing similarity measures.
Specifically, the idea of using heat diffusion on a hypersphere to measure
similarity has been previously proposed, demonstrating promising results based
on a heuristic heat kernel obtained from the zeroth order parametrix expansion;
however, how well this heuristic kernel agrees with the exact hyperspherical
heat kernel remains unknown. This paper presents a higher order parametrix
expansion of the heat kernel on a unit hypersphere and discusses several
problems associated with this expansion method. We then compare the heuristic
kernel with an exact form of the heat kernel expressed in terms of a uniformly
and absolutely convergent series in high-dimensional angular momentum
eigenmodes. Being a natural measure of similarity between sample points
dwelling on a hypersphere, the exact kernel often shows superior performance in
kernel SVM classifications applied to text mining, tumor somatic mutation
imputation, and stock market analysis
Exploring Automated Essay Scoring for Nonnative English Speakers
Automated Essay Scoring (AES) has been quite popular and is being widely
used. However, lack of appropriate methodology for rating nonnative English
speakers' essays has meant a lopsided advancement in this field. In this paper,
we report initial results of our experiments with nonnative AES that learns
from manual evaluation of nonnative essays. For this purpose, we conducted an
exercise in which essays written by nonnative English speakers in test
environment were rated both manually and by the automated system designed for
the experiment. In the process, we experimented with a few features to learn
about nuances linked to nonnative evaluation. The proposed methodology of
automated essay evaluation has yielded a correlation coefficient of 0.750 with
the manual evaluation.Comment: Accepted for publication at EUROPHRAS 201
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