5,672 research outputs found
Who is not multilingual now?
What is the relationship between research into multilingualism and research concerned more generally with language and communication in mathematics education? Diversity in linguistic practices is universal in modern society and poses problems for teaching and learning even in apparently monolingual contexts. Research in multilingualism and mathematics education offers constructs and insights that can inform research and pedagogy more widely. Th
What is a definition for in school mathematics?
This paper discusses the place of definitions in school mathematics, considering official UK curriculum guidance, literature related to definitions in advanced mathematical thinking and to experimental teaching focused on student development of definitions. A two dimensional framework is suggested for considering their functions, the ways in which students are expected to relate to them and their didactic purposes. Two contrasting examples of definitions from textbooks are analysed using systemic-functional linguistic tools
Storage of phase-coded patterns via STDP in fully-connected and sparse network: a study of the network capacity
We study the storage and retrieval of phase-coded patterns as stable
dynamical attractors in recurrent neural networks, for both an analog and a
integrate-and-fire spiking model. The synaptic strength is determined by a
learning rule based on spike-time-dependent plasticity, with an asymmetric time
window depending on the relative timing between pre- and post-synaptic
activity. We store multiple patterns and study the network capacity.
For the analog model, we find that the network capacity scales linearly with
the network size, and that both capacity and the oscillation frequency of the
retrieval state depend on the asymmetry of the learning time window. In
addition to fully-connected networks, we study sparse networks, where each
neuron is connected only to a small number z << N of other neurons. Connections
can be short range, between neighboring neurons placed on a regular lattice, or
long range, between randomly chosen pairs of neurons. We find that a small
fraction of long range connections is able to amplify the capacity of the
network. This imply that a small-world-network topology is optimal, as a
compromise between the cost of long range connections and the capacity
increase.
Also in the spiking integrate and fire model the crucial result of storing
and retrieval of multiple phase-coded patterns is observed. The capacity of the
fully-connected spiking network is investigated, together with the relation
between oscillation frequency of retrieval state and window asymmetry
Corner wetting in a far-from-equilibrium magnetic growth model
The irreversible growth of magnetic films is studied in three-dimensional
confined geometries of size , where is the growing
direction. Competing surface magnetic fields, applied to opposite corners of
the growing system, lead to the observation of a localization-delocalization
(weakly rounded) transition of the interface between domains of up and down
spins on the planes transverse to the growing direction. This effective
transition is the precursor of a true far-from-equilibrium corner wetting
transition that takes place in the thermodynamic limit. The phenomenon is
characterized quantitatively by drawing a magnetic field-temperature phase
diagram, firstly for a confined sample of finite size, and then by
extrapolating results, obtained with samples of different size, to the
thermodynamic limit. The results of this work are a nonequilibrium realization
of analogous phenomena recently investigated in equilibrium systems, such as
corner wetting transitions in the Ising model.Comment: 14 pages, 8 figures. EPJ styl
Models of the Knee in the Energy Spectrum of Cosmic Rays
The origin of the knee in the energy spectrum of cosmic rays is an
outstanding problem in astroparticle physics. Numerous mechanisms have been
proposed to explain the structure in the all-particle spectrum. In the article
basic ideas of several models are summarized, including diffusive acceleration
of cosmic rays in shock fronts, acceleration via cannonballs, leakage from the
Galaxy, interactions with background particles in the interstellar medium, as
well as new high-energy interactions in the atmosphere. The calculated energy
spectra and mean logarithmic masses are compiled and compared to results from
direct and indirect measurements.Comment: 30 pages, 20 figures accepted by Astroparticle Physics captions of
figures 1-3 clarified, references adde
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