3,069 research outputs found
The Importance of Forgetting: Limiting Memory Improves Recovery of Topological Characteristics from Neural Data
We develop of a line of work initiated by Curto and Itskov towards
understanding the amount of information contained in the spike trains of
hippocampal place cells via topology considerations. Previously, it was
established that simply knowing which groups of place cells fire together in an
animal's hippocampus is sufficient to extract the global topology of the
animal's physical environment. We model a system where collections of place
cells group and ungroup according to short-term plasticity rules. In
particular, we obtain the surprising result that in experiments with spurious
firing, the accuracy of the extracted topological information decreases with
the persistence (beyond a certain regime) of the cell groups. This suggests
that synaptic transience, or forgetting, is a mechanism by which the brain
counteracts the effects of spurious place cell activity
Pointwise convergence topology and function spaces in fuzzy analysis
We study the space of all continuous fuzzy-valued functions from a space into the space of fuzzy numbers (\mathbb{E}\sp{1},d\sb{\infty}) endowed with the pointwise convergence topology. Our results generalize the classical ones for continuous real-valued functions. The field of applications of this approach seems to be large, since the classical case allows many known devices to be fitted to general topology, functional analysis, coding theory, Boolean rings, etc
Conference Program
Document provides a list of the sessions, speakers, workshops, and committees of the 32nd Summer Conference on Topology and Its Applications
On algebraic supergroups, coadjoint orbits and their deformations
In this paper we study algebraic supergroups and their coadjoint orbits as
affine algebraic supervarieties. We find an algebraic deformation quantization
of them that can be related to the fuzzy spaces of non commutative geometry.Comment: 37 pages, AMS-LaTe
The baryon vertex with magnetic flux
In this letter we generalise the baryon vertex configuration of AdS/CFT by
adding a suitable instantonic magnetic field on its worldvolume, dissolving
D-string charge. A careful analysis of the configuration shows that there is an
upper bound on the number of dissolved strings. This should be a manifestation
of the stringy exclusion principle. We provide a microscopical description of
this configuration in terms of a dielectric effect for the dissolved strings.Comment: 17 pages, 2 figures. V2: reference added. V3: version to appear in
JHE
A Gauge Theory on Fuzzy Extra Dimensions
In this article, we explore the low energy structure of a gauge theory
over spaces with fuzzy sphere(s) as extra dimensions. In particular, we
determine the equivariant parametrization of the gauge fields, which transform
either invariantly or as vectors under the combined action of rotations
of the fuzzy spheres and those gauge transformations generated by carrying the spin irreducible representation of . The
cases of a single fuzzy sphere and a particular direct sum of
concentric fuzzy spheres, , covering the monopole bundle
sectors with windings are treated in full and the low energy degrees of
freedom for the gauge fields are obtained. Employing the parametrizations of
the fields in the former case, we determine a low energy action by tracing over
the fuzzy sphere and show that the emerging model is abelian Higgs type with
gauge symmetry and possess vortex solutions on , which we discuss in some detail. Generalization of our formulation to
the equivariant parametrization of gauge fields in theories is also
briefly addressed.Comment: 27+1 page
Symmetry Breaking and Order in the Age of Quasicrystals
The discovery of quasicrystals has changed our view of some of the most basic
notions related to the condensed state of matter. Before the age of
quasicrystals, it was believed that crystals break the continuous translation
and rotation symmetries of the liquid-phase into a discrete lattice of
translations, and a finite group of rotations. Quasicrystals, on the other
hand, possess no such symmetries-there are no translations, nor, in general,
are there any rotations, leaving them invariant. Does this imply that no
symmetry is left, or that the meaning of symmetry should be revised? We review
this and other questions related to the liquid-to-crystal symmetry-breaking
transition using the notion of indistinguishability. We characterize the
order-parameter space, describe the different elementary excitations, phonons
and phasons, and discuss the nature of dislocations-keeping in mind that we are
now living in the age of quasicrystals.Comment: To appear in a special issue on quasicrystals of The Israel Journal
of Chemistry, in celebration of the 2011 Nobel Prize in Chemistr
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