337 research outputs found
Abstract Tensor Systems as Monoidal Categories
The primary contribution of this paper is to give a formal, categorical
treatment to Penrose's abstract tensor notation, in the context of traced
symmetric monoidal categories. To do so, we introduce a typed, sum-free version
of an abstract tensor system and demonstrate the construction of its associated
category. We then show that the associated category of the free abstract tensor
system is in fact the free traced symmetric monoidal category on a monoidal
signature. A notable consequence of this result is a simple proof for the
soundness and completeness of the diagrammatic language for traced symmetric
monoidal categories.Comment: Dedicated to Joachim Lambek on the occasion of his 90th birthda
A categorification of the Casimir of quantum sl(2)
We categorify the Casimir element of the idempotented form of quantum sl(2).Comment: 63 pages, xypic diagrams. v2 corrects typo
Sums over Graphs and Integration over Discrete Groupoids
We show that sums over graphs such as appear in the theory of Feynman
diagrams can be seen as integrals over discrete groupoids. From this point of
view, basic combinatorial formulas of the theory of Feynman diagrams can be
interpreted as pull-back or push-forward formulas for integrals over suitable
groupoids.Comment: 27 pages, 4 eps figures; LaTeX2e; uses Xy-Pic. Some ambiguities
fixed, and several proofs simplifie
Correlating matched-filter model for analysis and optimisation of neural networks
A new formalism is described for modelling neural networks by means of which a clear physical understanding of the network behaviour can be gained. In essence, the neural net is represented by an equivalent network of matched filters which is then analysed by standard correlation techniques. The procedure is demonstrated on the synchronous Little-Hopfield network. It is shown how the ability of this network to discriminate between stored binary, bipolar codes is optimised if the stored codes are chosen to be orthogonal. However, such a choice will not often be possible and so a new neural network architecture is proposed which enables the same discrimination to be obtained for arbitrary stored codes. The most efficient convergence of the synchronous Little-Hopfield net is obtained when the neurons are connected to themselves with a weight equal to the number of stored codes. The processing gain is presented for this case. The paper goes on to show how this modelling technique can be extended to analyse the behaviour of both hard and soft neural threshold responses and a novel time-dependent threshold response is described
The Impact of Non-Equipartition on Cosmological Parameter Estimation from Sunyaev-Zel'dovich Surveys
The collisionless accretion shock at the outer boundary of a galaxy cluster
should primarily heat the ions instead of electrons since they carry most of
the kinetic energy of the infalling gas. Near the accretion shock, the density
of the intracluster medium is very low and the Coulomb collisional timescale is
longer than the accretion timescale. Electrons and ions may not achieve
equipartition in these regions. Numerical simulations have shown that the
Sunyaev-Zel'dovich observables (e.g., the integrated Comptonization parameter
Y) for relaxed clusters can be biased by a few percent. The Y-mass relation can
be biased if non-equipartition effects are not properly taken into account.
Using a set of hydrodynamical simulations, we have calculated three potential
systematic biases in the Y-mass relations introduced by non-equipartition
effects during the cross-calibration or self-calibration when using the galaxy
cluster abundance technique to constraint cosmological parameters. We then use
a semi-analytic technique to estimate the non-equipartition effects on the
distribution functions of Y (Y functions) determined from the extended
Press-Schechter theory. Depending on the calibration method, we find that
non-equipartition effects can induce systematic biases on the Y functions, and
the values of the cosmological parameters Omega_8, sigma_8, and the dark energy
equation of state parameter w can be biased by a few percent. In particular,
non-equipartition effects can introduce an apparent evolution in w of a few
percent in all of the systematic cases we considered. Techniques are suggested
to take into account the non-equipartition effect empirically when using the
cluster abundance technique to study precision cosmology. We conclude that
systematic uncertainties in the Y-mass relation of even a few percent can
introduce a comparable level of biases in cosmological parameter measurements.Comment: 10 pages, 3 figures, accepted for publication in the Astrophysical
Journal, abstract abridged slightly. Typos corrected in version
Higher Algebraic Structures and Quantization
We derive (quasi-)quantum groups in 2+1 dimensional topological field theory
directly from the classical action and the path integral. Detailed computations
are carried out for the Chern-Simons theory with finite gauge group. The
principles behind our computations are presumably more general. We extend the
classical action in a d+1 dimensional topological theory to manifolds of
dimension less than d+1. We then ``construct'' a generalized path integral
which in d+1 dimensions reduces to the standard one and in d dimensions
reproduces the quantum Hilbert space. In a 2+1 dimensional topological theory
the path integral over the circle is the category of representations of a
quasi-quantum group. In this paper we only consider finite theories, in which
the generalized path integral reduces to a finite sum. New ideas are needed to
extend beyond the finite theories treated here.Comment: 62 pages + 16 figures (revised version). In this revision we make
some small corrections and clarification
Surveying drifting icebergs and ice islands: Deterioration detection and mass estimation with aerial photogrammetry and laser scanning
Icebergs and ice islands (large, tabular icebergs) are challenging targets to survey due to their size, mobility, remote locations, and potentially difficult environmental conditions. Here, we assess the precision and utility of aerial photography surveying with structure-from-motion multi-view stereo photogrammetry processing (SfM) and vessel-based terrestrial laser scanning (TLS) for iceberg deterioration detection and mass estimation. For both techniques, we determine the minimum amount of change required to reliably resolve iceberg deterioration, the deterioration detection threshold (DDT), using triplicate surveys of two iceberg survey targets. We also calculate their relative uncertainties for iceberg mass estimation. The quality of deployed Global Positioning System (GPS) units that were used for drift correction and scale assignment was a major determinant of point cloud precision. When dual-frequency GPS receivers were deployed, DDT values of 2.5 and 0.40 m were calculated for the TLS and SfM point clouds, respectively. In contrast, values of 6.6 and 3.4 m were calculated when tracking beacons with lower-quality GPS were used. The SfM dataset was also more precise when used for iceberg mass estimation, and we recommend further development of this technique for iceberg-related end-uses
An Exploration of Fetish Social Networks and Communities
Online Social Networks (OSNs) provide a venue for virtual interactions and relationships between individuals. In some communities, OSNs also facilitate arranging offline meetings and relationships. FetLife, the world’s largest anonymous social network for the BDSM, fetish and kink communities, provides a unique example of an OSN that serves as an interaction space, community organizing tool, and sexual market. In this paper, we present a first look at the characteristics of European members of Fetlife, comprising 504,416 individual nodes with 1,912,196 connections. We looked at user characteristics in terms of gender, sexual orientation, and preferred role. We further examined the homophilic communities and find that women in particular are far more platonically involved on the site than straight males. Our results suggest there are important differences between the FetLife community and conventional OSNs
On coalgebras with internal moves
In the first part of the paper we recall the coalgebraic approach to handling
the so-called invisible transitions that appear in different state-based
systems semantics. We claim that these transitions are always part of the unit
of a certain monad. Hence, coalgebras with internal moves are exactly
coalgebras over a monadic type. The rest of the paper is devoted to supporting
our claim by studying two important behavioural equivalences for state-based
systems with internal moves, namely: weak bisimulation and trace semantics.
We continue our research on weak bisimulations for coalgebras over order
enriched monads. The key notions used in this paper and proposed by us in our
previous work are the notions of an order saturation monad and a saturator. A
saturator operator can be intuitively understood as a reflexive, transitive
closure operator. There are two approaches towards defining saturators for
coalgebras with internal moves. Here, we give necessary conditions for them to
yield the same notion of weak bisimulation.
Finally, we propose a definition of trace semantics for coalgebras with
silent moves via a uniform fixed point operator. We compare strong and weak
bisimilation together with trace semantics for coalgebras with internal steps.Comment: Article: 23 pages, Appendix: 3 page
The homotopy theory of simplicial props
The category of (colored) props is an enhancement of the category of colored
operads, and thus of the category of small categories. In this paper, the
second in a series on "higher props," we show that the category of all small
colored simplicial props admits a cofibrantly generated model category
structure. With this model structure, the forgetful functor from props to
operads is a right Quillen functor.Comment: Final version, to appear in Israel J. Mat
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