25,577 research outputs found
Constructing Fuzzy Time Series Model Using Combination of Table Lookup and Singular Value Decomposition Methods and Its Application to Forecasting Inflation Rate
Fuzzy time series is a dynamic process with linguistic values as its observations. Modelling fuzzy time series data developed by some researchers used discrete membership functions and table lookup method from training data. This paper presents a new method to modelling fuzzy time series data combining table lookup and singular value decomposition methods using continuous membership functions. Table lookup method is used to construct fuzzy relations from training data. Singular value decomposition of firing strength matrix and QR factorization are used to reduce fuzzy relations. Furthermore, this method is applied to forecast inflation rate in Indonesia based on six-factors one-order fuzzy time series. This result is compared with neural network method and the proposed method gets a higher forecasting accuracy rate than the neural network method
A projective Dirac operator on CP^2 within fuzzy geometry
We propose an ansatz for the commutative canonical spin_c Dirac operator on
CP^2 in a global geometric approach using the right invariant (left action-)
induced vector fields from SU(3). This ansatz is suitable for noncommutative
generalisation within the framework of fuzzy geometry. Along the way we
identify the physical spinors and construct the canonical spin_c bundle in this
formulation. The chirality operator is also given in two equivalent forms.
Finally, using representation theory we obtain the eigenspinors and calculate
the full spectrum. We use an argument from the fuzzy complex projective space
CP^2_F based on the fuzzy analogue of the unprojected spin_c bundle to show
that our commutative projected spin_c bundle has the correct
SU(3)-representation content.Comment: reduced to 27 pages, minor corrections, minor improvements, typos
correcte
2D fuzzy Anti-de Sitter space from matrix models
We study the fuzzy hyperboloids AdS^2 and dS^2 as brane solutions in matrix
models. The unitary representations of SO(2,1) required for quantum field
theory are identified, and explicit formulae for their realization in terms of
fuzzy wavefunctions are given. In a second part, we study the (A)dS^2 brane
geometry and its dynamics, as governed by a suitable matrix model. In
particular, we show that trace of the energy-momentum tensor of matter induces
transversal perturbations of the brane and of the Ricci scalar. This leads to a
linearized form of Henneaux-Teitelboim-type gravity, illustrating the mechanism
of emergent gravity in matrix models.Comment: 25 page
Fuzzy circle and new fuzzy sphere through confining potentials and energy cutoffs
Guided by ordinary quantum mechanics we introduce new fuzzy spheres of
dimensions d=1,2: we consider an ordinary quantum particle in D=d+1 dimensions
subject to a rotation invariant potential well V(r) with a very sharp minimum
on a sphere of unit radius. Imposing a sufficiently low energy cutoff to
`freeze' the radial excitations makes only a finite-dimensional Hilbert
subspace accessible and on it the coordinates noncommutative \`a la Snyder; in
fact, on it they generate the whole algebra of observables. The construction is
equivariant not only under rotations - as Madore's fuzzy sphere -, but under
the full orthogonal group O(D). Making the cutoff and the depth of the well
dependent on (and diverging with) a natural number L, and keeping the leading
terms in 1/L, we obtain a sequence S^d_L of fuzzy spheres converging (in a
suitable sense) to the sphere S^d as L diverges (whereby we recover ordinary
quantum mechanics on S^d). These models may be useful in condensed matter
problems where particles are confined on a sphere by an (at least
approximately) rotation-invariant potential, beside being suggestive of
analogous mechanisms in quantum field theory or quantum gravity.Comment: Latex file, 43 pages, 2 figures. We have added references and made
other minor improvements. To appear in J. Geom. Phy
Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
We generalise the construction of fuzzy CP^N in a manner that allows us to
access all noncommutative equivariant complex vector bundles over this space.
We give a simplified construction of polarization tensors on S^2 that
generalizes to complex projective space, identify Laplacians and natural
noncommutative covariant derivative operators that map between the modules that
describe noncommuative sections. In the process we find a natural
generalization of the Schwinger-Jordan construction to su(n) and identify
composite oscillators that obey a Heisenberg algebra on an appropriate Fock
space.Comment: 34 pages, v2 contains minor corrections to the published versio
New Fuzzy Extra Dimensions from Gauge Theories
We start with an Yang-Mills theory on a manifold ,
suitably coupled to two distinct set of scalar fields in the adjoint
representation of , which are forming a doublet and a triplet,
respectively under a global symmetry. We show that a direct sum of
fuzzy spheres emerges as the vacuum solution after the spontaneous breaking of the
gauge symmetry and lay the way for us to interpret the spontaneously broken
model as a gauge theory over . Focusing
on a gauge theory we present complete parameterizations of the
-equivariant, scalar, spinor and vector fields characterizing the
effective low energy features of this model. Next, we direct our attention to
the monopole bundles over with winding numbers ,
which naturally come forth through certain projections of , and
discuss the low energy behaviour of the gauge theory over . We study models with -component multiplet of the
global , give their vacuum solutions and obtain a class of winding
number monopole bundles as certain
projections of these vacuum solutions. We make the observation that is indeed the bosonic part of the fuzzy supersphere with
supersymmetry and construct the generators of the Lie superalgebra
in two of its irreducible representations using the matrix content of the
vacuum solution . Finally, we show that our vacuum solutions
are stable by demonstrating that they form mixed states with non-zero von
Neumann entropy.Comment: 27+1 pages, revised version, added references and corrected typo
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