997 research outputs found
Slow equivariant lump dynamics on the two sphere
The low-energy, rotationally equivariant dynamics of n CP^1 lumps on S^2 is
studied within the approximation of geodesic motion in the moduli space of
static solutions. The volume and curvature properties of this moduli space are
computed. By lifting the geodesic flow to the completion of an n-fold cover of
the moduli space, a good understanding of nearly singular lump dynamics within
this approximation is obtained.Comment: 12 pages, 3 figure
Characterization of the Crab Pulsar's Timing Noise
We present a power spectral analysis of the Crab pulsar's timing noise,
mainly using radio measurements from Jodrell Bank taken over the period
1982-1989. The power spectral analysis is complicated by nonuniform data
sampling and the presence of a steep red power spectrum that can distort power
spectra measurement by causing severe power ``leakage''. We develop a simple
windowing method for computing red noise power spectra of uniformly sampled
data sets and test it on Monte Carlo generated sample realizations of red
power-law noise. We generalize time-domain methods of generating power-law red
noise with even integer spectral indices to the case of noninteger spectral
indices. The Jodrell Bank pulse phase residuals are dense and smooth enough
that an interpolation onto a uniform time series is possible. A windowed power
spectrum is computed revealing a periodic or nearly periodic component with a
period of about 568 days and a 1/f^3 power-law noise component with a noise
strength of 1.24 +/- 0.067 10^{-16} cycles^2/sec^2 over the analysis frequency
range 0.003 - 0.1 cycles/day. This result deviates from past analyses which
characterized the pulse phase timing residuals as either 1/f^4 power-law noise
or a quasiperiodic process. The analysis was checked using the Deeter
polynomial method of power spectrum estimation that was developed for the case
of nonuniform sampling, but has lower spectral resolution. The timing noise is
consistent with a torque noise spectrum rising with analysis frequency as f
implying blue torque noise, a result not predicted by current models of pulsar
timing noise. If the periodic or nearly periodic component is due to a binary
companion, we find a companion mass > 3.2 Earth masses.Comment: 53 pages, 9 figures, submitted to MNRAS, abstract condense
Spectral Analysis of Guanine and Cytosine Fluctuations of Mouse Genomic DNA
We study global fluctuations of the guanine and cytosine base content (GC%)
in mouse genomic DNA using spectral analyses. Power spectra S(f) of GC%
fluctuations in all nineteen autosomal and two sex chromosomes are observed to
have the universal functional form S(f) \sim 1/f^alpha (alpha \approx 1) over
several orders of magnitude in the frequency range 10^-7< f < 10^-5 cycle/base,
corresponding to long-ranging GC% correlations at distances between 100 kb and
10 Mb. S(f) for higher frequencies (f > 10^-5 cycle/base) shows a flattened
power-law function with alpha < 1 across all twenty-one chromosomes. The
substitution of about 38% interspersed repeats does not affect the functional
form of S(f), indicating that these are not predominantly responsible for the
long-ranged multi-scale GC% fluctuations in mammalian genomes. Several
biological implications of the large-scale GC% fluctuation are discussed,
including neutral evolutionary history by DNA duplication, chromosomal bands,
spatial distribution of transcription units (genes), replication timing, and
recombination hot spots.Comment: 15 pages (figures included), 2 figure
Identifying phase synchronization clusters in spatially extended dynamical systems
We investigate two recently proposed multivariate time series analysis
techniques that aim at detecting phase synchronization clusters in spatially
extended, nonstationary systems with regard to field applications. The starting
point of both techniques is a matrix whose entries are the mean phase coherence
values measured between pairs of time series. The first method is a mean field
approach which allows to define the strength of participation of a subsystem in
a single synchronization cluster. The second method is based on an eigenvalue
decomposition from which a participation index is derived that characterizes
the degree of involvement of a subsystem within multiple synchronization
clusters. Simulating multiple clusters within a lattice of coupled Lorenz
oscillators we explore the limitations and pitfalls of both methods and
demonstrate (a) that the mean field approach is relatively robust even in
configurations where the single cluster assumption is not entirely fulfilled,
and (b) that the eigenvalue decomposition approach correctly identifies the
simulated clusters even for low coupling strengths. Using the eigenvalue
decomposition approach we studied spatiotemporal synchronization clusters in
long-lasting multichannel EEG recordings from epilepsy patients and obtained
results that fully confirm findings from well established neurophysiological
examination techniques. Multivariate time series analysis methods such as
synchronization cluster analysis that account for nonlinearities in the data
are expected to provide complementary information which allows to gain deeper
insights into the collective dynamics of spatially extended complex systems
Dualities for modal algebras from the point of view of triples
In this paper we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on the other. Furthermore, we investigate the monoidal structure induced by Cartesian product on the relational side and show that in some cases the corresponding operation on the algebraic side represents bimorphisms
Point process model of 1/f noise versus a sum of Lorentzians
We present a simple point process model of noise, covering
different values of the exponent . The signal of the model consists of
pulses or events. The interpulse, interevent, interarrival, recurrence or
waiting times of the signal are described by the general Langevin equation with
the multiplicative noise and stochastically diffuse in some interval resulting
in the power-law distribution. Our model is free from the requirement of a wide
distribution of relaxation times and from the power-law forms of the pulses. It
contains only one relaxation rate and yields spectra in a wide
range of frequency. We obtain explicit expressions for the power spectra and
present numerical illustrations of the model. Further we analyze the relation
of the point process model of noise with the Bernamont-Surdin-McWhorter
model, representing the signals as a sum of the uncorrelated components. We
show that the point process model is complementary to the model based on the
sum of signals with a wide-range distribution of the relaxation times. In
contrast to the Gaussian distribution of the signal intensity of the sum of the
uncorrelated components, the point process exhibits asymptotically a power-law
distribution of the signal intensity. The developed multiplicative point
process model of noise may be used for modeling and analysis of
stochastic processes in different systems with the power-law distribution of
the intensity of pulsing signals.Comment: 23 pages, 10 figures, to be published in Phys. Rev.
Dynamic Critical Behavior of the Swendsen-Wang Algorithm: The Two-Dimensional 3-State Potts Model Revisited
We have performed a high-precision Monte Carlo study of the dynamic critical
behavior of the Swendsen-Wang algorithm for the two-dimensional 3-state Potts
model. We find that the Li-Sokal bound ()
is almost but not quite sharp. The ratio seems to diverge
either as a small power () or as a logarithm.Comment: 35 pages including 3 figures. Self-unpacking file containing the
LaTeX file, the needed macros (epsf.sty, indent.sty, subeqnarray.sty, and
eqsection.sty) and the 3 Postscript figures. Revised version fixes a
normalization error in \xi (with many thanks to Wolfhard Janke for finding
the error!). To be published in J. Stat. Phys. 87, no. 1/2 (April 1997
Swimming against the tide: A case study of an integrated social studies department
A recent trend in developed countries’ school curricula has been the transition from disciplinary to generic forms of knowledge, resulting in an emphasis on interdisciplinary organisation and more active forms of learning. Subject specialists are increasingly expected to demonstrate how their subject interconnects and equips pupils with key life skills. Such a change requires a major cultural shift and has been controversial, particularly in Scotland where Curriculum for Excellence, the latest curriculum reform, has seen this debate re-emerge. A detailed empirical case study of one secondary school Social Studies department that has already negotiated these shifts is presented. The case study provides insights into how school and department structures and cultures conducive to a more integrated approach have been developed. Leadership, increased opportunities for teachers to exercise greater autonomy in their work, sources of impetus and support for innovation, and the co-construction of meaning through dialogue are important themes in this process. This case study connects with current policy and provides an insight into strategies that other schools might employ when seeking to embed integrative practices. The department is identified as a significant locus for innovation and one which appears to challenge the norm
When assessment defines the content—understanding goals in between teachers and policy
© 2020 The Authors. The Curriculum Journal published by John Wiley & Sons Ltd on behalf of British Educational Research Association.Education policy development internationally reflect a widespread expansion of learning outcome orientation in policy, curricula and assessment. In this paper, teachers’ perceptions about their work are explored, as goals and assessment play a more prominent role driven by the introduction of a learning outcomes‐oriented system. This is investigated through interviews of Norwegian teachers and extensive policy analysis of Norwegian policy documents. The findings indicate that the teachers are finding ways to negotiate and adjust to the language in the policies investigated in this study. Furthermore, the findings show that the teachers have developed their professional language according to the policies. The teachers referred to their self‐made criteria and goal sheets as central tools in explicating what is to be learned. In many ways, the tools for assessment, thus determine the content of education as well as what is valued in the educational system.publishedVersio
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