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.

Fatigue Behavior of a Cross-Ply Ceramic Matrix Composite at Elevated Temperature under Tension-Tension Loading

This study investigated the fatigue behavior and damage mechanisms of a [0-90]4s SiC-MAS ceramic matrix composite under tension-tension loading at two elevated temperatures and two frequencies. Stress and strain hystereses, maximum and minimum strain, and modulus of elasticity were evaluated to characterize the material behavior. Microscopy and fractography were used to evaluate damage progression and mechanisms. Fatigue life was independent of frequency at both temperatures

Bijectional, Generic and Permutational models of ZF

The consistency assumption of ZF implies the existence of a model (K,(epsilon)) for ZF by virtue of Goedel\u27s completeness theorem. But then von Neumann\u27s hierarchy (V(,a))(,a)(epsilon)(,R), where R is the class of all ordinals of K, implies the existence of a model (V,(epsilon)) for ZFG, where G is the Axiom of Regularity. This shows that the consistency of G with ZF can be proven by means of an inner model with methods which can be formalized in ZF. Similarly, Goedel\u27s model (L,(epsilon)) of constructible sets and Cohen\u27s minimal model (M,(epsilon)) of strongly constructible sets are inner models of (V,(epsilon)) satisfying ZFG + (V = L) and consequently satisfying ZFG + GCH, and thus ZFG + GCH + AC. As in the case of inner models, a natural tendency for construcing various ZF models is to consider the class of sets of (K,(epsilon)) that satisfy a set-theoretical formula R(x). But then, because of the minimality of (M,(epsilon)), no such inner model can be constructed for ZFG + (NOT) (V = L) and hence for ZFG + (NOT) AC or for ZFG + (NOT) CH;Thus, to construct ZFG models in which V = L is not valid, one must use methods which go beyond ZF, i.e. which cannot be formalized in ZF. Examples of such models are the Bijectional, Generic and Permutational models which we consider in this dissertation;First, we construct Bijectional and Dyadic Sequential ZF models with sets having k atoms for any cardinal k and ZF models with the negation of the Extensionality Axiom;We also construct standard models MG of ZF where G is not an element of M. To this end we introduce the notion of an elementhood relation with respect to a suitable generic subset G of a partially ordered set P of M and consider the corresponding partially-order-valued class of progenitors. We then find the quotient class of progenitors with respect to G to obtain MG. Moreover, we obtain some results concerning the cardinalities of the dense subsets of partially ordered sets. Furthermore, we give necessary and sufficient conditions for the existence of generic subsets of partially ordered sets by means of the notion of molecule;Using some of the above results, we consider Permutational models based on decreasing chains of equivalence classes of permutations and construct a model for ZF and (NOT) AC

Pure hydrogen low-temperature plasma exposure of HOPG and graphene: Graphane formation?

Single- and multilayer graphene and highly ordered pyrolytic graphite (HOPG) were exposed to a pure hydrogen low-temperature plasma (LTP). Characterizations include various experimental techniques such as photoelectron spectroscopy, Raman spectroscopy and scanning probe microscopy. Our photoemission measurement shows that hydrogen LTP exposed HOPG has a diamond-like valence-band structure, which suggests double-sided hydrogenation. With the scanning tunneling microscopy technique, various atomic-scale charge-density patterns were observed, which may be associated with different C-H conformers. Hydrogen-LTP-exposed graphene on SiO₂ has a Raman spectrum in which the D peak to G peak ratio is over 4, associated with hydrogenation on both sides. A very low defect density was observed in the scanning probe microscopy measurements, which enables a reverse transformation to graphene. Hydrogen-LTP-exposed HOPG possesses a high thermal stability, and therefore, this transformation requires annealing at over 1000 °C

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

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