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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
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 and . 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 and 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
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