Browsing Pure & Applied Mathematics (Scholarly Publications) by Author "HOUGHTON, CONOR JAMES"
Now showing items 1-20 of 26
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A comment on "A fast L_p spike alignment metric" by A. J. Dubbs, B. A. Seiler and M. O. Magnasco [arXiv:0907.3137]
(2009)Measuring the transmitted information in metric-based clustering has become something of a standard test for the performance of a spike train metric. In this comment, the recently proposed L_p Victor-Purpura metric is used ... -
The effect of pion mass on Skyrme configurations
(2007)In the Skyrme model, atomic nuclei are identified with solitonic configurations. If the pion mass is set to zero, these configurations are spherical shells of energy with a fullerene-like appearance and are well approximated ... -
Finding community structures in networks by playing pass-the-parcel.
(2008)Many data sets can be represented by undirected networks. Often, an interesting and important feature of these networks is the existence of communities; groups of nodes whose interconnectivity is higher than the average ... -
Folding in the Skyrme model.
(American Institute of Physics, 2001)There are only three stable singularities of a differentiable map between three-dimensional manifolds, namely folds, cusps and swallowtails. A Skyrme configuration is a map from space to SU2, and its singularities correspond ... -
Icosahedral Skyrmions
(American Institute of Physics, 2003)In this article we aim to determine the baryon numbers at which the minimal energy Skyrmion has icosahedral symmetry. By comparing polyhedra which arise as minimal energy Skyrmions with the dual of polyhedra that minimize ... -
Instanton vibrations of the 3-Skyrmion
(American Physical Society, 1999)The Atiyah-Drinfeld-Hitchin-Manin matrix corresponding to a tetrahedrally symmetric 3-instanton is calculated. Some small variations of the matrix correspond to vibrations of the instanton-generated 3-Skyrmion. These ... -
Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold
(IOP, 1996)We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah?Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole ... -
A metric space approach to the information capacity of spike trains
(2010)Classical information theory can be either discrete or continuous, corresponding to discrete or continuous random variables. However, although spike times in a spike train are described by continuous variables, the ... -
Multicloud solutions with massless and massive monopoles.
(American Physical Society, 2002)Certain spontaneously broken gauge theories contain massless magnetic monopoles. These are realized classically as clouds of non-Abelian fields surrounding one or more massive monopoles. In order to gain a better understanding ... -
Nahm data and the mass of 1/4-BPS states
(American Physical Society, 2000)The mass of 1 / 4-BPS dyonic configurations in N=4 D=4 supersymmetric Yang-Mills theories is calculated within the Nahm formulation. The SU(3) example, with two massive monopoles and one massless monopole, is considered ... -
New hyper-Kaehler manifolds by fixing monopoles
(American Physical Society, 1997)The construction of new hyper-Ka?hler manifolds by taking the infinite monopole mass limit of certain Bogomol?nyi-Prasad-Sommerfield monopole moduli spaces is considered. The one-parameter family of hyper- Ka?hler manifolds ... -
A new multi-neuron spike-train metric
(MIT Press, 2008)The Victor-Purpura spike-train metric has recently been extended to a family of multi-neuron metrics and used to analyze spike trains recorded simultaneously from pairs of proximate neurons. The Victor- Purpura metric ... -
Octahedral and dodecahedral monopoles
(IOP, 1996)It is shown that there exists a charge five monopole with octahedral symmetry and a charge seven monopole with icosahedral symmetry. A numerical implementation of the ADHMN construction is used to calculate the energy ... -
On the constraints defining BPS monopoles
(Springer Science and Business Media, 2000)We discuss the explicit formulation of the transcendental constraints defining spectral curves of SU.2/ BPS monopoles in the twistor approach of Hitchin, following Ercolani and Sinha. We obtain an improved version of the ... -
Pulsation and precession of the resonant swinging spring
(Elsevier, 2004)When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio 2:1, there is a regular exchange of energy between the two modes of oscillation. We refer to this ... -
Skyrmions and monopoles: dihedrally-symmetric 3-solitons.
(Met, 2001)The similarity between Skyrmions and Bogomolny-Prasad-Sommerfield (BPS) monopoles has often been remarked. In this talk I will illustrate this similarity by reviewing the rational map ansatz and by discussing the specific ... -
Sparse coding of birdsong and receptive field structure in songbirds
(2009)Auditory neurons can be characterized by a spectro-temporal receptive field, the kernel of a linear filter model describing the neuronal response to a stimulus. With a view to better understanding the tuning properties ... -
The sparse decomposition of sound in the time domain using non-negative quadratic programming.
(2009)Non-negative matrix deconvolution and sparse decomposition are useful tools for source separation and acoustic object recognition. Here, a new algorithm for calculating a sparse decomposition of sound in the time domain ... -
Studying spike trains using a van Rossum metric with a synapse-like filter
(2009)Spike trains are unreliable. For example, in the primary sensory areas, spike patterns and precise spike times will vary between responses to the same stimulus. Nonetheless, information about sensory inputs is communicated ...
