16,246 research outputs found
The binned bispectrum estimator: template-based and non-parametric CMB non-Gaussianity searches
We describe the details of the binned bispectrum estimator as used for the
official 2013 and 2015 analyses of the temperature and polarization CMB maps
from the ESA Planck satellite. The defining aspect of this estimator is the
determination of a map bispectrum (3-point correlator) that has been binned in
harmonic space. For a parametric determination of the non-Gaussianity in the
map (the so-called fNL parameters), one takes the inner product of this binned
bispectrum with theoretically motivated templates. However, as a complementary
approach one can also smooth the binned bispectrum using a variable smoothing
scale in order to suppress noise and make coherent features stand out above the
noise. This allows one to look in a model-independent way for any statistically
significant bispectral signal. This approach is useful for characterizing the
bispectral shape of the galactic foreground emission, for which a theoretical
prediction of the bispectral anisotropy is lacking, and for detecting a
serendipitous primordial signal, for which a theoretical template has not yet
been put forth. Both the template-based and the non-parametric approaches are
described in this paper.Comment: Latex 42 pages with 10 figures and JCAP macros. v2: corrected small
mistake in section 5.3, changed colour scale of slice figures, other minor
changes and additions, matches published versio
Robust predictions for an oscillatory bispectrum in Planck 2015 data from transient reductions in the speed of sound of the inflaton
We update the search for features in the Cosmic Microwave Background (CMB)
power spectrum due to transient reductions in the speed of sound, using Planck
2015 CMB temperature and polarisation data. We enlarge the parameter space to
much higher oscillatory frequencies of the feature, and define a robust prior
independent of the ansatz for the reduction, guaranteed to reproduce the
assumptions of the theoretical model and exhaustive in the regime in which the
feature is easily distinguishable from the baseline cosmology. We find a fit to
the -- minus/plus structure in Planck TT power spectrum, as
well as features spanning along the higher 's (--).
For the last ones, we compute the correlated features that we expect to find in
the CMB bispectrum, and asses their signal-to-noise and correlation to the
ISW-lensing secondary bispectrum. We compare our findings to the shape-agnostic
oscillatory template tested in Planck 2015, and we comment on some tantalising
coincidences with some of the traits described in Planck's 2015 bispectrum
data.Comment: 19 pages - matches published versio
Singular value decomposition applied to compact binary coalescence gravitational-wave signals
We investigate the application of the singular value decomposition to
compact-binary, gravitational-wave data-analysis. We find that the truncated
singular value decomposition reduces the number of filters required to analyze
a given region of parameter space of compact binary coalescence waveforms by an
order of magnitude with high reconstruction accuracy. We also compute an
analytic expression for the expected signal-loss due to the singular value
decomposition truncation.Comment: 4 figures, 6 page
Computing Node Polynomials for Plane Curves
According to the G\"ottsche conjecture (now a theorem), the degree N^{d,
delta} of the Severi variety of plane curves of degree d with delta nodes is
given by a polynomial in d, provided d is large enough. These "node
polynomials" N_delta(d) were determined by Vainsencher and Kleiman-Piene for
delta <= 6 and delta <= 8, respectively. Building on ideas of Fomin and
Mikhalkin, we develop an explicit algorithm for computing all node polynomials,
and use it to compute N_delta(d) for delta <= 14. Furthermore, we improve the
threshold of polynomiality and verify G\"ottsche's conjecture on the optimal
threshold up to delta <= 14. We also determine the first 9 coefficients of
N_delta(d), for general delta, settling and extending a 1994 conjecture of Di
Francesco and Itzykson.Comment: 23 pages; to appear in Mathematical Research Letter
Automating embedded analysis capabilities and managing software complexity in multiphysics simulation part I: template-based generic programming
An approach for incorporating embedded simulation and analysis capabilities
in complex simulation codes through template-based generic programming is
presented. This approach relies on templating and operator overloading within
the C++ language to transform a given calculation into one that can compute a
variety of additional quantities that are necessary for many state-of-the-art
simulation and analysis algorithms. An approach for incorporating these ideas
into complex simulation codes through general graph-based assembly is also
presented. These ideas have been implemented within a set of packages in the
Trilinos framework and are demonstrated on a simple problem from chemical
engineering
A Logical Product Approach to Zonotope Intersection
We define and study a new abstract domain which is a fine-grained combination
of zonotopes with polyhedric domains such as the interval, octagon, linear
templates or polyhedron domain. While abstract transfer functions are still
rather inexpensive and accurate even for interpreting non-linear computations,
we are able to also interpret tests (i.e. intersections) efficiently. This
fixes a known drawback of zonotopic methods, as used for reachability analysis
for hybrid sys- tems as well as for invariant generation in abstract
interpretation: intersection of zonotopes are not always zonotopes, and there
is not even a best zonotopic over-approximation of the intersection. We
describe some examples and an im- plementation of our method in the APRON
library, and discuss some further in- teresting combinations of zonotopes with
non-linear or non-convex domains such as quadratic templates and maxplus
polyhedra
Synthesis and Optimization of Reversible Circuits - A Survey
Reversible logic circuits have been historically motivated by theoretical
research in low-power electronics as well as practical improvement of
bit-manipulation transforms in cryptography and computer graphics. Recently,
reversible circuits have attracted interest as components of quantum
algorithms, as well as in photonic and nano-computing technologies where some
switching devices offer no signal gain. Research in generating reversible logic
distinguishes between circuit synthesis, post-synthesis optimization, and
technology mapping. In this survey, we review algorithmic paradigms ---
search-based, cycle-based, transformation-based, and BDD-based --- as well as
specific algorithms for reversible synthesis, both exact and heuristic. We
conclude the survey by outlining key open challenges in synthesis of reversible
and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table
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