4,333 research outputs found
Using Big Bang Nucleosynthesis to Extend CMB Probes of Neutrino Physics
We present calculations showing that upcoming Cosmic Microwave Background
(CMB) experiments will have the power to improve on current constraints on
neutrino masses and provide new limits on neutrino degeneracy parameters. The
latter could surpass those derived from Big Bang Nucleosynthesis (BBN) and the
observationally-inferred primordial helium abundance. These conclusions derive
from our Monte Carlo Markov Chain (MCMC) simulations which incorporate a full
BBN nuclear reaction network. This provides a self-consistent treatment of the
helium abundance, the baryon number, the three individual neutrino degeneracy
parameters and other cosmological parameters. Our analysis focuses on the
effects of gravitational lensing on CMB constraints on neutrino rest mass and
degeneracy parameter. We find for the PLANCK experiment that total (summed)
neutrino mass eV could be ruled out at or better.
Likewise neutrino degeneracy parameters and could be detected or ruled out at
confidence, or better. For POLARBEAR we find that the corresponding detectable
values are , , and , while for EPIC we obtain ,
, and . Our forcast for
EPIC demonstrates that CMB observations have the potential to set constraints
on neutrino degeneracy parameters which are better than BBN-derived limits and
an order of magnitude better than current WMAP-derived limits.Comment: 27 pages, 11 figures, matches published version in JCA
Autocorrelation of Random Matrix Polynomials
We calculate the autocorrelation functions (or shifted moments) of the
characteristic polynomials of matrices drawn uniformly with respect to Haar
measure from the groups U(N), O(2N) and USp(2N). In each case the result can be
expressed in three equivalent forms: as a determinant sum (and hence in terms
of symmetric polynomials), as a combinatorial sum, and as a multiple contour
integral. These formulae are analogous to those previously obtained for the
Gaussian ensembles of Random Matrix Theory, but in this case are identities for
any size of matrix, rather than large-matrix asymptotic approximations. They
also mirror exactly autocorrelation formulae conjectured to hold for
L-functions in a companion paper. This then provides further evidence in
support of the connection between Random Matrix Theory and the theory of
L-functions
Spectral Statistics of "Cellular" Billiards
For a bounded planar domain whose boundary contains a number of
flat pieces we consider a family of non-symmetric billiards
constructed by patching several copies of along 's. It is
demonstrated that the length spectrum of the periodic orbits in is
degenerate with the multiplicities determined by a matrix group . We study
the energy spectrum of the corresponding quantum billiard problem in
and show that it can be split in a number of uncorrelated subspectra
corresponding to a set of irreducible representations of . Assuming
that the classical dynamics in are chaotic, we derive a
semiclassical trace formula for each spectral component and show that their
energy level statistics are the same as in standard Random Matrix ensembles.
Depending on whether is real, pseudo-real or complex, the spectrum
has either Gaussian Orthogonal, Gaussian Symplectic or Gaussian Unitary types
of statistics, respectively.Comment: 18 pages, 4 figure
The absent-present researcher: data analysis of pre-recorded parent-driven campaign videos
In recent years, there has been a proliferation of sophisticated, user-friendly and accessible instruments of video data collection (e.g. mobile/cell phones and tablets) which facilitate video-based research and analysis. This paper reports on the opportunities and challenges of undertaking video analysis by reporting on the qualitative video analysis of a subset of 30 purposively selected videos from #notanurse_but, a parent-driven video campaign initiated by WellChild, a UK charity. This paper provides insight into one way of conducting video analysis, appreciating that a variety of approaches exist and that methodological reflections on analytical work with video recordings are limited. The authors critically consider researcher subjectivity; the everydayness of video data; making assumptions; and the incomplete picture provided by video data. Despite notable limitations to the approach of video analysis as a standalone method, the authors conclude that video analysis is capable of eliciting data that may not otherwise be obtained
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The Journey to R4D: An institutional history of an Australian Initiative on Food Security in Africa
Internal Revie
Random matrix theory, the exceptional Lie groups, and L-functions
There has recently been interest in relating properties of matrices drawn at
random from the classical compact groups to statistical characteristics of
number-theoretical L-functions. One example is the relationship conjectured to
hold between the value distributions of the characteristic polynomials of such
matrices and value distributions within families of L-functions. These
connections are here extended to non-classical groups. We focus on an explicit
example: the exceptional Lie group G_2. The value distributions for
characteristic polynomials associated with the 7- and 14-dimensional
representations of G_2, defined with respect to the uniform invariant (Haar)
measure, are calculated using two of the Macdonald constant term identities. A
one parameter family of L-functions over a finite field is described whose
value distribution in the limit as the size of the finite field grows is
related to that of the characteristic polynomials associated with the
7-dimensional representation of G_2. The random matrix calculations extend to
all exceptional Lie groupsComment: 14 page
Complex System Governance as a Framework for Asset Management
Complex system governance (CSG) is an emerging field encompassing a framework for system performance improvement through the purposeful design, execution, and evolution of essential metasystem functions. The goal of this study was to understand how the domain of asset management (AsM) can leverage the capabilities of CSG. AsM emerged from engineering as a structured approach to organizing complex organizations to realize the value of assets while balancing performance, risks, costs, and other opportunities. However, there remains a scarcity of literature discussing the potential relationship between AsM and CSG. To initiate the closure of this gap, this research reviews the basics of AsM and the methods associated with realizing the value of assets. Then, the basics of CSG are provided along with how CSG might be leveraged to support AsM. We conclude the research with the implications for AsM and suggested future research
Rate of convergence of linear functions on the unitary group
We study the rate of convergence to a normal random variable of the real and
imaginary parts of Tr(AU), where U is an N x N random unitary matrix and A is a
deterministic complex matrix. We show that the rate of convergence is O(N^{-2 +
b}), with 0 <= b < 1, depending only on the asymptotic behaviour of the
singular values of A; for example, if the singular values are non-degenerate,
different from zero and O(1) as N -> infinity, then b=0. The proof uses a
Berry-Esse'en inequality for linear combinations of eigenvalues of random
unitary, matrices, and so appropriate for strongly dependent random variables.Comment: 34 pages, 1 figure; corrected typos, added remark 3.3, added 3
reference
Applications and generalizations of Fisher-Hartwig asymptotics
Fisher-Hartwig asymptotics refers to the large form of a class of
Toeplitz determinants with singular generating functions. This class of
Toeplitz determinants occurs in the study of the spin-spin correlations for the
two-dimensional Ising model, and the ground state density matrix of the
impenetrable Bose gas, amongst other problems in mathematical physics. We give
a new application of the original Fisher-Hartwig formula to the asymptotic
decay of the Ising correlations above , while the study of the Bose gas
density matrix leads us to generalize the Fisher-Hartwig formula to the
asymptotic form of random matrix averages over the classical groups and the
Gaussian and Laguerre unitary matrix ensembles. Another viewpoint of our
generalizations is that they extend to Hankel determinants the Fisher-Hartwig
asymptotic form known for Toeplitz determinants.Comment: 25 page
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