913 research outputs found
Tools or crutches? Apparatus as a sense-making aid in mathematics teaching with children with moderate learning difficulties
This paper challenges a view of concrete materials as abstracts used within a rigid instructional sequence that particular children are perceived to require or not, as the case may be. Focussing on mathematics teaching, it contends that it is more useful to consider the function of these materials as tools, artefacts used flexibly and selectively by pupils to make sense of mathematics, rather than as crutches, devices which may support procedural competency in mathematics but with no guarantees of understanding
High-Resolution Simulations of Cosmic Microwave Background non-Gaussian Maps in Spherical Coordinates
We describe a new numerical algorithm to obtain high-resolution simulated
maps of the Cosmic Microwave Background (CMB), for a broad class of
non-Gaussian models. The kind of non-Gaussianity we account for is based on the
simple idea that the primordial gravitational potential is obtained by a
non-linear but local mapping from an underlying Gaussian random field, as
resulting from a variety of inflationary models. Our technique, which is based
on a direct realization of the potential in spherical coordinates and fully
accounts for the radiation transfer function, allows to simulate non-Gaussian
CMB maps down to the Planck resolution (), with
reasonable memory storage and computational time.Comment: 9 pages, 5 figures. Submitted to ApJ. A version with higher quality
figures is available at http://www.pd.infn.it/~liguori/content.htm
'I like it instead of maths' : how pupils with moderate learning difficulties in Scottish primary special schools intuitively solved mathematical word problems
This study shows how a group of 24 children in three Scottish primary schools for pupils with moderate learning difficulties responded to word problems following their teachers' introduction to the principles of Cognitively Guided Instruction (CGI). CGI is a professional development programme in mathematics instruction based on constructivist principles developed at the University of Wisconsin-Madison. The study found that the sample group of pupils were able to develop their understanding of mathematical concepts through actively engaging in word problems without prior explicit instruction and with minimal teacher adjustments. The pupils' conceptual understandings demonstrated by their solution strategies within CGI activities were generally not consistent with classroom records of assessment. The results were encouraging in illustrating the capacity of the sample group of pupils with moderate learning difficulties to reveal their mathematical thinking and considers the importance of this insight for instructional decision making
Constraining Primordial Magnetic Fields with Future Cosmic Shear Surveys
The origin of astrophysical magnetic fields observed in galaxies and clusters
of galaxies is still unclear. One possibility is that primordial magnetic
fields generated in the early Universe provide seeds that grow through
compression and turbulence during structure formation. A cosmological magnetic
field present prior to recombination would produce substantial matter
clustering at intermediate/small scales, on top of the standard inflationary
power spectrum. In this work we study the effect of this alteration on one
particular cosmological observable, cosmic shear. We adopt the semi-analytic
halo model in order to describe the non-linear clustering of matter, and feed
it with the altered mass variance induced by primordial magnetic fields. We
find that the convergence power spectrum is, as expected, substantially
enhanced at intermediate/small angular scales, with the exact amplitude of the
enhancement depending on the magnitude and power-law index of the magnetic
field power spectrum. We use the predicted statistical errors for a future
wide-field cosmic shear survey, on the model of the ESA Cosmic Vision mission
\emph{Euclid}, in order to forecast constraints on the amplitude of primordial
magnetic fields as a function of the spectral index. We find that the amplitude
will be constrained at the level of nG for , and at the
level of nG for . The latter is at the same level of
lower bounds coming from the secondary emission of gamma-ray sources, implying
that for high spectral indices \emph{Euclid} will certainly be able to detect
primordial magnetic fields, if they exist. The present study shows how
large-scale structure surveys can be used for both understanding the origins of
astrophysical magnetic fields and shedding new light on the physics of the
pre-recombination Universe. (abridged)Comment: 24 pages, 9 figures. To appear on JCA
X-ray and Sunyaev-Zel'dovich scaling relations in galaxy clusters
[Abridged] We present an analysis of the scaling relations between X-ray
properties and Sunyaev-Zel'dovich (SZ) parameters for a sample of 24 X-ray
luminous galaxy clusters observed with Chandra and with measured SZ effect.
These objects are in the redshift range 0.14--0.82 and have X-ray bolometric
luminosity L>10^45 erg/s. We perform a spatially resolved spectral analysis and
recover the density, temperature and pressure profiles of the ICM, just relying
on the spherical symmetry of the cluster and the hydrostatic equilibrium
hypothesis. We observe that the correlations among X-ray quantities only are in
agreement with previous results obtained for samples of high-z X-ray luminous
galaxy clusters. On the relations involving SZ quantities, we obtain that they
correlate with the gas temperature with a logarithmic slope significantly
larger than the predicted value from the self-similar model. The measured
scatter indicates, however, that the central Compton parameter y_0 is a proxy
of the gas temperature at the same level of other X-ray quantities like
luminosity. Our results on the X-ray and SZ scaling relations show a tension
between the quantities more related to the global energy of the system (e.g.
gas temperature, gravitating mass) and the indicators of the structure of the
ICM (e.g. gas density profile, central Compton parameter y_0), showing the most
significant deviations from the values of the slope predicted from the
self-similar model in the L-T, L-M_{tot}, M_{gas}-T, y_0-T relations. When the
slope is fixed to the self-similar value, these relations consistently show a
negative evolution suggesting a scenario in which the ICM at higher redshift
has lower both X-ray luminosity and pressure in the central regions than the
expectations from self-similar model.Comment: MNRAS in press - Minor revision to match published versio
Primordial density perturbations with running spectral index: impact on non-linear cosmic structures
(abridged) We explore the statistical properties of non-linear cosmic
structures in a flat CDM cosmology in which the index of the
primordial power spectrum for scalar perturbations is allowed to depend on the
scale. Within the inflationary paradigm, the running of the scalar spectral
index can be related to the properties of the inflaton potential, and it is
hence of critical importance to test it with all kinds of observations, which
cover the linear and non-linear regime of gravitational instability. We focus
on the amount of running allowed by an updated
combination of CMB anisotropy data and the 2dF Galaxy Redshift Survey. Our
analysis constrains
at 95% Confidence Level when (not) taking into
account primordial gravitational waves in a ratio as predicted by canonical
single field inflation, in agreement with other works. For the cosmological
models best fitting the data both with and without running we studied the
abundance of galaxy clusters and of rare objects, the halo bias, the
concentration of dark matter halos, the Baryon Acoustic Oscillation, the power
spectrum of cosmic shear, and the Integrated Sachs-Wolfe effect. We find that
counting galaxy clusters in future X-ray and Sunyaev-Zel'dovich surveys could
discriminate between the two models, more so if broad redshift information
about the cluster samples will be available. Likewise, measurements of the
power spectrum of cosmological weak lensing as performed by planned all-sky
optical surveys such as EUCLID could detect a running of the primordial
spectral index, provided the uncertainties about the source redshift
distribution and the underlying matter power spectrum are well under control.Comment: 17 pages, 14 figures, 4 tables. Accepted for publication on MNRA
Inclusion and education in the United Kingdom
Paper describes inclusion and education in the United Kingdom
Imprints of primordial non-Gaussianity on the number counts of cosmic shear peaks
We studied the effect of primordial non-Gaussianity with varied bispectrum
shapes on the number counts of signal-to-noise peaks in wide field cosmic shear
maps. The two cosmological contributions to this particular weak lensing
statistic, namely the chance projection of Large Scale Structure and the
occurrence of real, cluster-sized dark matter halos, have been modeled
semi-analytically, thus allowing to easily introduce the effect of non-Gaussian
initial conditions. We performed a Fisher matrix analysis by taking into
account the full covariance of the peak counts in order to forecast the joint
constraints on the level of primordial non-Gaussianity and the amplitude of the
matter power spectrum that are expected by future wide field imaging surveys.
We find that positive-skewed non-Gaussianity increases the number counts of
cosmic shear peaks, more so at high signal-to-noise values, where the signal is
mostly dominated by massive clusters as expected. The increment is at the level
of ~1 for f_NL=10 and ~10 for f_NL=100 for a local shape of the primordial
bispectrum, while different bispectrum shapes give generically a smaller
effect. For a future survey on the model of the proposed ESA space mission
Euclid and by avoiding the strong assumption of being capable to distinguish
the weak lensing signal of galaxy clusters from chance projection of Large
Scale Structures we forecasted a 1-sigma error on the level of non-Gaussianity
of ~30-40 for the local and equilateral models, and of ~100-200 for the less
explored enfolded and orthogonal bispectrum shapes.Comment: 13 pages, 8 figures, 1 table. Submitted to MNRA
'Letting the children lead: The Jeely Nursery' - A second interim report for the Robertson Trust
This is the second interim report undertaken for the Robertson Trust of an ongoing project developed by the Jeely Nursery (JN) in Castlemilk, Glasgow, from 2007-10
Constraints on extended quintessence from high-redshift Supernovae
We obtain constraints on quintessence models from magnitude-redshift
measurements of 176 type Ia Supernovae. The considered quintessence models are
ordinary quintessence, with Ratra-Peebles and SUGRA potentials, and extended
quintessence with a Ratra-Peebles potential. We compute confidence regions in
the plane and find that for SUGRA potentials it is not
possible to obtain useful constraints on these parameters; for the
Ratra-Peebles case, both for the extended and ordinary quintessence we find
\alpha\mincir 0.8, at the level. We also consider simulated dataset
for the SNAP satellite for the same models: again, for a SUGRA potential it
will not be possible to obtain constraints on , while with a
Ratra-Peebles potential its value will be determined with an error \mincir
0.6. We evaluate the inaccuracy made by approximating the time evolution of
the equation of state with a linear or constant w\diz, instead of using its
exact redshift evolution. Finally we discuss the effects of different
systematic errors in the determination of quintessence parameters.Comment: 8 pages, ApJ in press. We added a discussion of the systematic errors
and we updated the SNe catalogu
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