168,048 research outputs found
On the integration of digital technologies into mathematics classrooms
Trouche‘s (2003) presentation at the Third Computer Algebra in Mathematics Education Symposium focused on the notions of instrumental genesis and of orchestration: the former concerning the mutual transformation of learner and artefact in the course of constructing knowledge with technology; the latter concerning the problem of integrating technology into classroom practice. At the Symposium, there was considerable discussion of the idea of situated abstraction, which the current authors have been developing over the last decade. In this paper, we summarise the theory of instrumental genesis and attempt to link it with situated abstraction. We then seek to broaden Trouche‘s discussion of orchestration to elaborate the role of artefacts in the process, and describe how the notion of situated abstraction could be used to make sense of the evolving mathematical knowledge of a community as well as an individual. We conclude by elaborating the ways in which technological artefacts can provide shared means of mathematical expression, and discuss the need to recognise the diversity of student‘s emergent meanings for mathematics, and the legitimacy of mathematical expression that may be initially divergent from institutionalised mathematics
Computer simulation of shear flows of granular material
The purpose of this paper is to present results from computer simulations of Couette flows of granular materials and to examine the detailed rheological behavior inherent in these simulations. Comparison is made with the experimental results of Bagnold (1954) and Savage and Sayed (1980, 1982) as well as with the various theoretical constitutive models
Beyond the storage capacity: data driven satisfiability transition
Data structure has a dramatic impact on the properties of neural networks,
yet its significance in the established theoretical frameworks is poorly
understood. Here we compute the Vapnik-Chervonenkis entropy of a kernel machine
operating on data grouped into equally labelled subsets. At variance with the
unstructured scenario, entropy is non-monotonic in the size of the training
set, and displays an additional critical point besides the storage capacity.
Remarkably, the same behavior occurs in margin classifiers even with randomly
labelled data, as is elucidated by identifying the synaptic volume encoding the
transition. These findings reveal aspects of expressivity lying beyond the
condensed description provided by the storage capacity, and they indicate the
path towards more realistic bounds for the generalization error of neural
networks.Comment: 5 pages, 2 figure
Volume-Enclosing Surface Extraction
In this paper we present a new method, which allows for the construction of
triangular isosurfaces from three-dimensional data sets, such as 3D image data
and/or numerical simulation data that are based on regularly shaped, cubic
lattices. This novel volume-enclosing surface extraction technique, which has
been named VESTA, can produce up to six different results due to the nature of
the discretized 3D space under consideration. VESTA is neither template-based
nor it is necessarily required to operate on 2x2x2 voxel cell neighborhoods
only. The surface tiles are determined with a very fast and robust construction
technique while potential ambiguities are detected and resolved. Here, we
provide an in-depth comparison between VESTA and various versions of the
well-known and very popular Marching Cubes algorithm for the very first time.
In an application section, we demonstrate the extraction of VESTA isosurfaces
for various data sets ranging from computer tomographic scan data to simulation
data of relativistic hydrodynamic fireball expansions.Comment: 24 pages, 33 figures, 4 tables, final versio
Artificial life meets computational creativity?
I review the history of work in Artificial Life on the problem of the open-ended evolutionary growth of complexity in computational worlds. This is then put into the context of evolutionary epistemology and human creativity
On Termination for Faulty Channel Machines
A channel machine consists of a finite controller together with several fifo
channels; the controller can read messages from the head of a channel and write
messages to the tail of a channel. In this paper, we focus on channel machines
with insertion errors, i.e., machines in whose channels messages can
spontaneously appear. Such devices have been previously introduced in the study
of Metric Temporal Logic. We consider the termination problem: are all the
computations of a given insertion channel machine finite? We show that this
problem has non-elementary, yet primitive recursive complexity
Instrument development, data collection, and characteristics of practices, staff, and measures in the Improving Quality of Care in Diabetes (iQuaD) Study
Peer reviewedPublisher PD
The role of local structure in dynamical arrest
Amorphous solids, or glasses, are distinguished from crystalline solids by
their lack of long-range structural order. At the level of two-body structural
correlations, glassformers show no qualitative change upon vitrifying from a
supercooled liquid. Nonetheless the dynamical properties of a glass are so much
slower that it appears to take on the properties of a solid. While many
theories of the glass transition focus on dynamical quantities, a solid's
resistance to flow is often viewed as a consequence of its structure. Here we
address the viewpoint that this remains the case for a glass. Recent
developments using higher-order measures show a clear emergence of structure
upon dynamical arrest in a variety of glass formers and offer the tantalising
hope of a structural mechanism for arrest. However a rigorous fundamental
identification of such a causal link between structure and arrest remains
elusive. We undertake a critical survey of this work in experiments, computer
simulation and theory and discuss what might strengthen the link between
structure and dynamical arrest. We move on to highlight the relationship
between crystallisation and glass-forming ability made possible by this deeper
understanding of the structure of the liquid state, and emphasize the potential
to design materials with optimal glassforming and crystallisation ability, for
applications such as phase-change memory. We then consider aspects of the
phenomenology of glassy systems where structural measures have yet to make a
large impact, such as polyamorphism (the existence of multiple liquid states),
aging (the time-evolution of non-equilibrium materials below their glass
transition) and the response of glassy materials to external fields such as
shear.Comment: 70 page
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