Continued Progress: Promising Evidence on Personalized Learning

The findings are grouped into four sections. The first section on student achievement finds that there were positive effects on student mathematics and reading performance and that the lowest-performing students made substantial gains relative to their peers. The second section on implementation and the perceptions of stakeholders finds that adoption of personalized learning practices varied considerably. Personalized learning practices that are direct extensions of current practice were more common, but implementation of some of the more challenging personalized learning strategies was less common. The third section relates implementation features to outcomes and identifies three elements of personalized learning that were being implemented in tandem in the schools with the largest achievement effects. Finally, the fourth section compares teachers' and students' survey responses to a national sample and finds some differences, such as teachers' greater use of practices that support competency-based learning and greater use of technology for personalization in the schools in this study with implementation data

The effect of magnetic dipolar interactions on the interchain spin wave dispersion in CsNiF_3

Inelastic neutron scattering measurements were performed on the ferromagnetic chain system CsNiF_3 in the collinear antiferromagnetic ordered state below T_N = 2.67K. The measured spin wave dispersion was found to be in good agreement with linear spin wave theory including dipolar interactions. The additional dipole tensor in the Hamiltonian was essential to explain some striking phenomena in the measured spin wave spectrum: a peculiar feature of the dispersion relation is a jump at the zone center, caused by strong dipolar interactions in this system. The interchain exchange coupling constant and the planar anisotropy energy were determined within the present model to be J'/k_B = -0.0247(12)K and A/k_B = 3.3(1)K. This gives a ratio J/J' \approx 500, using the previously determined intrachain coupling constant J/k_B = 11.8$. The small exchange energy J' is of the same order as the dipolar energy, which implies a strong competition between the both interactions.Comment: 18 pages, TeX type, 7 Postscript figures included. To be published in Phys. Rev.

Categorification of persistent homology

We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.Comment: 27 pages, v3: minor changes, to appear in Discrete & Computational Geometr

Time-dependent galactic winds

Cosmic rays (CRs) are transported out of the galaxy by diffusion and advection due to streaming along magnetic field lines and resonant scattering off self-excited Magneto-Hydro-Dynamic (MHD) waves. Thus momentum is transferred to the plasma via the frozen-in waves as a mediator assisting the thermal pressure in driving a galactic wind. Galactic CRs (GCRs) are accelerated by shock waves generated in supernova remnants (SNRs), and they propagate from the disc into the halo. Therefore CR acceleration in the halo strongly depends on the inner disc boundary conditions. We performed hydrodynamical simulations of galactic winds in flux tube geometry appropriate for disc galaxies, describing the CR diffusive-advective transport in a hydrodynamical fashion (by taking appropriate moments of the Fokker-Planck equation) along with the energy exchange with self-generated MHD waves. Our time-dependent CR hydrodynamic simulations confirm that the evolution of galactic winds with feedback depends on the structure of the galactic halo. In case of a wind-structured halo, the wind breaks down after the last super nova (SN) has exploded. The mechanism described here offers a natural and elegant solution to explain the power-law distribution of CRs between the `knee' and the `ankle'. The transition will be naturally smooth, because the Galactic CRs accelerated at SN shocks will be `post-accelerated' by shocks generated at the inner boundary and travelling through the halo.Comment: Galaxies: evolution -- ISM: jets and outflows -- Galaxies: starburst -- supernova remnants -- cosmic ray

The Closest Look at 1H0707-495: X-ray Reverberation Lags with 1.3 Ms of Data

Reverberation lags in AGN were first discovered in the NLS1 galaxy, 1H0707-495. We present a follow-up analysis using 1.3 Ms of data, which allows for the closest ever look at the reverberation signature of this remarkable source. We confirm previous findings of a hard lag of ~100 seconds at frequencies v ~ [0.5 - 4] e-4 Hz, and a soft lag of ~30 seconds at higher frequencies, v ~ [0.6 - 3] e-3 Hz. These two frequency domains clearly show different energy dependences in their lag spectra. We also find evidence for a signature from the broad Fe K line in the high frequency lag spectrum. We use Monte Carlo simulations to show how the lag and coherence measurements respond to the addition of Poisson noise and to dilution by other components. With our better understanding of these effects on the lag, we show that the lag-energy spectra can be modelled with a scenario in which low frequency hard lags are produced by a compact corona responding to accretion rate fluctuations propagating through an optically thick accretion disc, and the high frequency soft lags are produced by short light-travel delay associated with reflection of coronal power-law photons off the disc.Comment: 11 pages, 10 figures. Accepted for publication in MNRA

A Parallax Distance to the Microquasar GRS 1915+105 and a Revised Estimate of its Black Hole Mass

Using the Very Long Baseline Array, we have measured a trigonometric parallax for the micro quasar GRS 1915+105, which contains a black hole and a K-giant companion. This yields a direct distance estimate of 8.6 (+2.0,-1.6) kpc and a revised estimate for the mass of the black hole of 12.4 (+2.0,-1.8) Msun. GRS 1915+105 is at about the same distance as some HII regions and water masers associated with high-mass star formation in the Sagittarius spiral arm of the Galaxy. The absolute proper motion of GRS 1915+105 is -3.19 +/- 0.03 mas/y and -6.24 +/- 0.05 mas/y toward the east and north, respectively, which corresponds to a modest peculiar speed of 22 +/-24 km/s at the parallax distance, suggesting that the binary did not receive a large velocity kick when the black hole formed. On one observational epoch, GRS 1915+105 displayed superluminal motion along the direction of its approaching jet. Considering previous observations of jet motions, the jet in GRS 1915+105 can be modeled with a jet inclination to the line of sight of 60 +/- 5 deg and a variable flow speed between 0.65c and 0.81c, which possibly indicates deceleration of the jet at distances from the black hole >2000 AU. Finally, using our measurements of distance and estimates of black hole mass and inclination, we provisionally confirm our earlier result that the black hole is spinning very rapidly.Comment: 20 pages; 2 tables; 6 figure

X-ray Spectral Analysis of the Steady States of GRS 1915+105

We report on the X-ray spectral behavior within the steady states of GRS 1915+105. Our work is based on the full data set on the source obtained using the Proportional Counter Array on the Rossi X-ray Timing Explorer and 15 GHz radio data obtained using the Ryle Telescope. The steady observations within the X-ray data set naturally separated into two regions in the color-color diagram and we refer to them as steady-soft and steady-hard. GRS 1915+105 displays significant curvature in the coronal component in both the soft and hard data within the {\it RXTE}/PCA bandpass. A majority of the steady-soft observations displays a roughly constant inner disk radius (R_in), while the steady-hard observations display an evolving disk truncation which is correlated to the mass accretion rate through the disk. The disk flux and coronal flux are strongly correlated in steady-hard observations and very weakly correlated in the steady-soft observations. Within the steady-hard observations we observe two particular circumstances when there are correlations between the coronal X-ray flux and the radio flux with log slopes \eta~0.68 +/- 0.35 and \eta ~ 1.12 +/- 0.13. They are consistent with the upper and lower tracks of Gallo et al. (2012), respectively. A comparison of model parameters to the state definitions show that almost all steady-soft observations match the criteria of either thermal or steep power law state, while a large portion of the steady-hard observations match the hard state criteria when the disk fraction constraint is neglected.Comment: 21 pages, 15 figures, 2 tables. Accepted for publication in Ap

Dualities in persistent (co)homology

We consider sequences of absolute and relative homology and cohomology groups that arise naturally for a filtered cell complex. We establish algebraic relationships between their persistence modules, and show that they contain equivalent information. We explain how one can use the existing algorithm for persistent homology to process any of the four modules, and relate it to a recently introduced persistent cohomology algorithm. We present experimental evidence for the practical efficiency of the latter algorithm.Comment: 16 pages, 3 figures, submitted to the Inverse Problems special issue on Topological Data Analysi

The Low-Spin Black Hole in LMC X-3

Building upon a new dynamical model for the X-ray binary LMC X-3, we measure the spin of its black hole primary via the continuum-fitting method. We consider over one thousand thermal-state RXTE X-ray spectra of LMC X-3. Using a large subset of these spectra, we constrain the spin parameter of the black hole to be spin = 0.21(+0.18,-0.22), 90% confidence. Our estimate of the uncertainty in spin takes into account a wide range of systematic errors. We discuss evidence for a correlation between a black hole's spin and the complexity of its X-ray spectrum.Comment: Submitted to ApJL, 5 pages emulateapj, 2 figures and 1 tabl