12,498 research outputs found
Fuzziness and Funds Allocation in Portfolio Optimization
Each individual investor is different, with different financial goals,
different levels of risk tolerance and different personal preferences. From the
point of view of investment management, these characteristics are often defined
as objectives and constraints. Objectives can be the type of return being
sought, while constraints include factors such as time horizon, how liquid the
investor is, any personal tax situation and how risk is handled. It's really a
balancing act between risk and return with each investor having unique
requirements, as well as a unique financial outlook - essentially a constrained
utility maximization objective. To analyze how well a customer fits into a
particular investor class, one investment house has even designed a structured
questionnaire with about two-dozen questions that each has to be answered with
values from 1 to 5. The questions range from personal background (age, marital
state, number of children, job type, education type, etc.) to what the customer
expects from an investment (capital protection, tax shelter, liquid assets,
etc.). A fuzzy logic system has been designed for the evaluation of the answers
to the above questions. We have investigated the notion of fuzziness with
respect to funds allocation.Comment: 21 page
Three Dimensional Quantum Geometry and Deformed Poincare Symmetry
We study a three dimensional non-commutative space emerging in the context of
three dimensional Euclidean quantum gravity. Our starting point is the
assumption that the isometry group is deformed to the Drinfeld double D(SU(2)).
We generalize to the deformed case the construction of the flat Euclidean space
as the quotient of its isometry group ISU(2) by SU(2). We show that the algebra
of functions becomes the non-commutative algebra of SU(2) distributions endowed
with the convolution product. This construction gives the action of ISU(2) on
the algebra and allows the determination of plane waves and coordinate
functions. In particular, we show that: (i) plane waves have bounded momenta;
(ii) to a given momentum are associated several SU(2) elements leading to an
effective description of an element in the algebra in terms of several physical
scalar fields; (iii) their product leads to a deformed addition rule of momenta
consistent with the bound on the spectrum. We generalize to the non-commutative
setting the local action for a scalar field. Finally, we obtain, using harmonic
analysis, another useful description of the algebra as the direct sum of the
algebra of matrices. The algebra of matrices inherits the action of ISU(2):
rotations leave the order of the matrices invariant whereas translations change
the order in a way we explicitly determine.Comment: latex, 37 page
Twistors, CFT and Holography
According to one of many equivalent definitions of twistors a (null) twistor
is a null geodesic in Minkowski spacetime. Null geodesics can intersect at
points (events). The idea of Penrose was to think of a spacetime point as a
derived concept: points are obtained by considering the incidence of twistors.
One needs two twistors to obtain a point. Twistor is thus a ``square root'' of
a point. In the present paper we entertain the idea of quantizing the space of
twistors. Twistors, and thus also spacetime points become operators acting in a
certain Hilbert space. The algebra of functions on spacetime becomes an
operator algebra. We are therefore led to the realm of non-commutative
geometry. This non-commutative geometry turns out to be related to conformal
field theory and holography. Our construction sheds an interesting new light on
bulk/boundary dualities.Comment: 21 pages, figure
Unbraiding the braided tensor product
We show that the braided tensor product algebra
of two module algebras of a quasitriangular Hopf algebra is
equal to the ordinary tensor product algebra of with a subalgebra of
isomorphic to , provided there exists a
realization of within . In other words, under this assumption we
construct a transformation of generators which `decouples' (i.e.
makes them commuting). We apply the theorem to the braided tensor product
algebras of two or more quantum group covariant quantum spaces, deformed
Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page
Conceptual Spaces in Object-Oriented Framework
The aim of this paper is to show that the middle level of
mental representations in a conceptual spaces framework is consistent
with the OOP paradigm. We argue that conceptual spaces framework
together with vague prototype theory of categorization appears to be
the most suitable solution for modeling the cognitive apparatus of
humans, and that the OOP paradigm can be easily and intuitively
reconciled with this framework. First, we show that the prototypebased
OOP approach is consistent with Gärdenfors’ model in terms
of structural coherence. Second, we argue that the product of cloning
process in a prototype-based model is in line with the structure of
categories in Gärdenfors’ proposal. Finally, in order to make the fuzzy
object-oriented model consistent with conceptual space, we
demonstrate how to define membership function in a more cognitive
manner, i.e. in terms of similarity to prototype
Quantum Spacetimes in the Year 1
We review certain emergent notions on the nature of spacetime from
noncommutative geometry and their radical implications. These ideas of
spacetime are suggested from developments in fuzzy physics, string theory, and
deformation quantisation. The review focuses on the ideas coming from fuzzy
physics. We find models of quantum spacetime like fuzzy on which states
cannot be localised, but which fluctuate into other manifolds like .
New uncertainty principles concerning such lack of localisability on quantum
spacetimes are formulated.Such investigations show the possibility of
formulating and answering questions like the probabilty of finding a point of a
quantum manifold in a state localised on another one. Additional striking
possibilities indicated by these developments is the (generic) failure of
theorem and the conventional spin-statistics connection. They even suggest that
Planck's `` constant '' may not be a constant, but an operator which does not
commute with all observables. All these novel possibilities arise within the
rules of conventional quantum physics,and with no serious input from gravity
physics.Comment: 11 pages, LaTeX; talks given at Utica and Kolkata .Minor corrections
made and references adde
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