12,498 research outputs found

    Fuzziness and Funds Allocation in Portfolio Optimization

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    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

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    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

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    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

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    We show that the braided tensor product algebra A1A2A_1\underline{\otimes}A_2 of two module algebras A1,A2A_1, A_2 of a quasitriangular Hopf algebra HH is equal to the ordinary tensor product algebra of A1A_1 with a subalgebra of A1A2A_1\underline{\otimes}A_2 isomorphic to A2A_2, provided there exists a realization of HH within A1A_1. In other words, under this assumption we construct a transformation of generators which `decouples' A1,A2A_1, A_2 (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

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    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

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    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 S4S^4 on which states cannot be localised, but which fluctuate into other manifolds like CP3 CP^3 . 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 CPTCPT 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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