3,609 research outputs found
Randomness in topological models
p. 914-925There are two aspects of randomness in topological models. In the first one, topological
idealization of random patterns found in the Nature can be regarded as planar
representations of three-dimensional lattices and thus reconstructed in the space. Another aspect of randomness is related to graphs in which some properties are determined in a random way. For example, combinatorial properties of graphs: number of vertices, number of edges, and connections between them can be regarded as events in the defined probability space. Random-graph theory deals with a question: at what connection probability a particular property reveals. Combination of probabilistic description of planar graphs and their spatial reconstruction creates new opportunities in structural form-finding, especially in the inceptive, the most creative, stage.Tarczewski, R.; Bober, W. (2010). Randomness in topological models. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/695
Topological Models of Columnar Vagueness
This paper intends to further the understanding of the formal properties of (higher-order) vagueness by connecting theories of (higher-order) vagueness with more recent work in topology. First, we provide a “translation” of Bobzien's account of columnar higher-order vagueness into the logic of topological spaces. Since columnar vagueness is an essential ingredient of her solution to the Sorites paradox, a central problem of any theory of vagueness comes into contact with the modern mathematical theory of topology. Second, Rumfitt’s recent topological reconstruction of Sainsbury’s theory of prototypically defined concepts is shown to lead to the same class of spaces that characterize Bobzien’s account of columnar vagueness, namely, weakly scattered spaces. Rumfitt calls these spaces polar spaces. They turn out to be closely related to Gärdenfors’ conceptual spaces, which have come to play an ever more important role in cognitive science and related disciplines. Finally, Williamson’s “logic of clarity” is explicated in terms of a generalized topology (“locology”) that can be considered an alternative to standard topology. Arguably, locology has some conceptual advantages over topology with respect to the conceptualization of a boundary and a borderline. Moreover, in Williamson’s logic of clarity, vague concepts with respect to a notion of a locologically inspired notion of a “slim boundary” are (stably) columnar. Thus, Williamson’s logic of clarity also exhibits a certain affinity for columnar vagueness. In sum, a topological perspective is useful for a conceptual elucidation and unification of central aspects of a variety of contemporary accounts of vagueness
Fermionic Coset Models as Topological Models
By considering the fermionic realization of coset models, we show that
the partition function for the model defines a Topological Quantum
Field Theory and coincides with that for a 2-dimensional Abelian BF system. In
the non-Abelian case, we prove the topological character of coset models
by explicit computation, also finding a natural extension of 2-dimensional BF
systems with non-Abelian symmetry.Comment: 14p
On the twisted G/H topological models
The twisted G/H models are constructed as twisted supersymmetric gauged WZW
models. We analyze the case of , with , and discuss possible
generalizations. We introduce a non-abelian bosonization of the ghost
system in the adjoint of and in G/H. By computing chiral anomalies in the
latter picture we write the quantum action as a decoupled sum of ``matter",
gauge and ghost sectors. The action is also derived in the unbosonized version.
We invoke a free field parametrization and extract the space of physical states
by computing the cohomology of , the sum of the BRST gauge-fixing charge
and the twisted supersymmetry charge. For a given we briefly discuss the
relation between the various G/H models corresponding to different choices of
. The choice corresponds to the topological G/G theory.Comment: 27 page
Prediction and Topological Models in Neuroscience
In the last two decades, philosophy of neuroscience has predominantly focused on explanation. Indeed, it has been argued that mechanistic models are the standards of explanatory success in neuroscience over, among other things, topological models. However, explanatory power is only one virtue of a scientific model. Another is its predictive power. Unfortunately, the notion of prediction has received comparatively little attention in the philosophy of neuroscience, in part because predictions seem disconnected from interventions. In contrast, we argue that topological predictions can and do guide interventions in science, both inside and outside of neuroscience. Topological models allow researchers to predict many phenomena, including diseases, treatment outcomes, aging, and cognition, among others. Moreover, we argue that these predictions also offer strategies for useful interventions. Topology-based predictions play this role regardless of whether they do or can receive a mechanistic interpretation. We conclude by making a case for philosophers to focus on prediction in neuroscience in addition to explanation alone
Constructing topological models by symmetrization: A PEPS study
Symmetrization of topologically ordered wavefunctions is a powerful method
for constructing new topological models. Here, we study wavefunctions obtained
by symmetrizing quantum double models of a group in the Projected Entangled
Pair States (PEPS) formalism. We show that symmetrization naturally gives rise
to a larger symmetry group which is always non-abelian. We prove
that by symmetrizing on sufficiently large blocks, one can always construct
wavefunctions in the same phase as the double model of . In order to
understand the effect of symmetrization on smaller patches, we carry out
numerical studies for the toric code model, where we find strong evidence that
symmetrizing on individual spins gives rise to a critical model which is at the
phase transitions of two inequivalent toric codes, obtained by anyon
condensation from the double model of .Comment: 10 pages. v2: accepted versio
Interacting six-dimensional topological field theories
We study the gauge-fixing and symmetries (BRST-invariance and vector
supersymmetry) of various six-dimensional topological models involving Abelian
or non-Abelian 2-form potentials.Comment: 11 page
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