2,771 research outputs found
Four-Dimensional Spin Foam Perturbation Theory
We define a four-dimensional spin-foam perturbation theory for the -theory with a potential term defined for a compact semi-simple
Lie group on a compact orientable 4-manifold . This is done by using the
formal spin foam perturbative series coming from the spin-foam generating
functional. We then regularize the terms in the perturbative series by passing
to the category of representations of the quantum group
where is the Lie algebra of and is a root of unity. The
Chain-Mail formalism can be used to calculate the perturbative terms when the
vector space of intertwiners , where is the
adjoint representation of , is 1-dimensional for each irrep
. We calculate the partition function in the dilute-gas limit for
a special class of triangulations of restricted local complexity, which we
conjecture to exist on any 4-manifold . We prove that the first-order
perturbative contribution vanishes for finite triangulations, so that we define
a dilute-gas limit by using the second-order contribution. We show that is
an analytic continuation of the Crane-Yetter partition function. Furthermore,
we relate to the partition function for the theory
A Cubical Set Approach to 2-Bundles with Connection and Wilson Surfaces
In the context of non-abelian gerbes we define a cubical version of
categorical group 2-bundles with connection over a smooth manifold. We define
their two-dimensional parallel transport, study its properties, and define
non-abelian Wilson surface functionals.Comment: Improvement on the exposition. Approximately 60 pages, 2 figure
Emergent Rhythmic Structures as Cultural Phenomena Driven by Social Pressure in a Society of Artificial Agents
This thesis studies rhythm from an evolutionary computation perspective. Rhythm is the most fundamental dimension of music and can be used as a ground to describe the evolution of music. More specifically, the main goal of the thesis is to investigate how complex rhythmic structures evolve, subject to the cultural transmission between individuals in a society. The study is developed by means of computer modelling and simulations informed by evolutionary computation and artificial life (A-Life). In this process, self-organisation plays a fundamental role. The evolutionary process is steered by the evaluation of rhythmic complexity and by the exposure to rhythmic material.
In this thesis, composers and musicologists will find the description of a system named A-Rhythm, which explores the emerged behaviours in a community of artificial autonomous agents that interact in a virtual environment. The interaction between the agents takes the form of imitation games.
A set of necessary criteria was established for the construction of a compositional system in which cultural transmission is observed. These criteria allowed the comparison with related work in the field of evolutionary computation and music.
In the development of the system, rhythmic representation is discussed. The proposed representation enabled the development of complexity and similarity based measures, and the recombination of rhythms in a creative manner. A-Rhythm produced results in the form of simulation data which were evaluated in terms of the coherence of repertoires of the agents. The data shows how rhythmic sequences are changed and sustained in the population, displaying synchronic and diachronic diversity. Finally, this tool was used as a generative mechanism for composition and several examples are presented.Leverhulme Trus
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