Open educational resources and teaching in the 21st century: questions concerning authority

As a source of materials for education the Web is, to a large extent, shifting ground. Open Educational Resources (OER) provided by Higher Education Institutions constitute, at least in principle, a reliable category of Web-based resources given their association with traditional forms of expert authority. Nevertheless, OER embody different aspects of academic thinking and practice, competing, in an unlevelled field, with other sources that may provide a much more immediate appeal in that they afford quick and easy consumption of information delivered in a piecemeal, often uncritical, fashion. This paper draws upon a piece of research in the area of ‘online informal learning’ to illustrate issues arising from the availability of open content and, in particular, OER. This research suggests a number of aspects related to the impact of open content on assumed boundaries between teacher/learner, formal/informal learning, training/education, content/presentation and, crucially, in how the blurring of these boundaries may have an impact on the location of ‘value’ within views of education in which marketing and business discourses predominate. The paper argues that, despite the need for critical debate on issues regarding validation, current arguments focusing on ‘expertise’ risk diluting its significance in subtle yet fundamental ways

Efficient Enumeration of Induced Subtrees in a K-Degenerate Graph

In this paper, we address the problem of enumerating all induced subtrees in an input k-degenerate graph, where an induced subtree is an acyclic and connected induced subgraph. A graph G = (V, E) is a k-degenerate graph if for any its induced subgraph has a vertex whose degree is less than or equal to k, and many real-world graphs have small degeneracies, or very close to small degeneracies. Although, the studies are on subgraphs enumeration, such as trees, paths, and matchings, but the problem addresses the subgraph enumeration, such as enumeration of subgraphs that are trees. Their induced subgraph versions have not been studied well. One of few example is for chordless paths and cycles. Our motivation is to reduce the time complexity close to O(1) for each solution. This type of optimal algorithms are proposed many subgraph classes such as trees, and spanning trees. Induced subtrees are fundamental object thus it should be studied deeply and there possibly exist some efficient algorithms. Our algorithm utilizes nice properties of k-degeneracy to state an effective amortized analysis. As a result, the time complexity is reduced to O(k) time per induced subtree. The problem is solved in constant time for each in planar graphs, as a corollary

Constraints on a Primordial Magnetic Field

We derive an upper limit of $B_0<3.4\times 10^{-9}(\Omega_0h_{50}^2)^{1/2}$ Gauss on the present strength of any primordial homogeneous magnetic field. The microwave background anisotropy created by cosmological magnetic fields is calculated in the most general flat and open anisotropic cosmologies containing expansion-rate and 3-curvature anisotropies. Our limit is derived from a statistical analysis of the 4-year Cosmic Background Explorer data for anisotropy patterns characteristic of homogeneous anisotropy averaged over all possible sky orientations with respect to the COBE receiver. The limits we obtain are considerably stronger than those imposed by primordial nucleosynthesis and ensure that other magnetic field effects on the microwave background structure are unobservably small.Comment: 4 pages, uses RevTex, submitted to PR

Explicit Actions for Electromagnetism with Two Gauge Fields with Only one Electric and one Magnetic Physical Fields

We extend the work of Mello et al. based in Cabbibo and Ferrari concerning the description of electromagnetism with two gauge fields from a variational principle, i.e. an action. We provide a systematic independent derivation of the allowed actions which have only one magnetic and one electric physical fields and are invariant under the discrete symmetries $P$ and $T$. We conclude that neither the Lagrangian, nor the Hamiltonian, are invariant under the electromagnetic duality rotations. This agrees with the weak-strong coupling mixing characteristic of the duality due to the Dirac quantization condition providing a natural way to differentiate dual theories related by the duality rotations (the energy is not invariant). Also the standard electromagnetic duality rotations considered in this work violate both $P$ and $T$ by inducing Hopf terms (theta terms) for each sector and a mixed Maxwell term. The canonical structure of the theory is briefly addressed and the 'magnetic' gauge sector is interpreted as a ghost sector.Comment: v2: 12 pages; References added, discussion concerning degrees of freedom corrected; v3: is now used the standard normalization of 1/4 in the actions; the possibility of theta being a pseudo-scalar implied a title changing; eq (23) added; signs corrected in equations (39,45-47); references adde

The Vector-Tensor nature of Bekenstein's relativistic theory of Modified Gravity

Bekenstein's theory of relativistic gravity is conventionally written as a bi-metric theory. The two metrics are related by a disformal transformation defined by a dynamical vector field and a scalar field. In this comment we show that the theory can be re-written as Vector-Tensor theory akin to Einstein-Aether theories with non-canonical kinetic terms. We discuss some of the implications of this equivalence.Comment: Updated version: Notation cleaned up and some typos corrected-TG

Are Magnetic Wind-Driving Disks Inherently Unstable?

There have been claims in the literature that accretion disks in which a centrifugally driven wind is the dominant mode of angular momentum transport are inherently unstable. This issue is considered here by applying an equilibrium-curve analysis to the wind-driving, ambipolar diffusion-dominated, magnetic disk model of Wardle & Konigl (1993). The equilibrium solution curves for this class of models typically exhibit two distinct branches. It is argued that only one of these branches represents unstable equilibria and that a real disk/wind system likely corresponds to a stable solution.Comment: 5 pages, 2 figures, to be published in ApJ, vol. 617 (2004 Dec 20). Uses emulateapj.cl