68,216 research outputs found

    Bayesian outlier detection in Capital Asset Pricing Model

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    We propose a novel Bayesian optimisation procedure for outlier detection in the Capital Asset Pricing Model. We use a parametric product partition model to robustly estimate the systematic risk of an asset. We assume that the returns follow independent normal distributions and we impose a partition structure on the parameters of interest. The partition structure imposed on the parameters induces a corresponding clustering of the returns. We identify via an optimisation procedure the partition that best separates standard observations from the atypical ones. The methodology is illustrated with reference to a real data set, for which we also provide a microeconomic interpretation of the detected outliers

    Partitioning de Bruijn Graphs into Fixed-Length Cycles for Robot Identification and Tracking

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    We propose a new camera-based method of robot identification, tracking and orientation estimation. The system utilises coloured lights mounted in a circle around each robot to create unique colour sequences that are observed by a camera. The number of robots that can be uniquely identified is limited by the number of colours available, qq, the number of lights on each robot, kk, and the number of consecutive lights the camera can see, \ell. For a given set of parameters, we would like to maximise the number of robots that we can use. We model this as a combinatorial problem and show that it is equivalent to finding the maximum number of disjoint kk-cycles in the de Bruijn graph dB(q,)\text{dB}(q,\ell). We provide several existence results that give the maximum number of cycles in dB(q,)\text{dB}(q,\ell) in various cases. For example, we give an optimal solution when k=q1k=q^{\ell-1}. Another construction yields many cycles in larger de Bruijn graphs using cycles from smaller de Bruijn graphs: if dB(q,)\text{dB}(q,\ell) can be partitioned into kk-cycles, then dB(q,)\text{dB}(q,\ell) can be partitioned into tktk-cycles for any divisor tt of kk. The methods used are based on finite field algebra and the combinatorics of words.Comment: 16 pages, 4 figures. Accepted for publication in Discrete Applied Mathematic

    Twist operator correlation functions in O(n) loop models

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    Using conformal field theoretic methods we calculate correlation functions of geometric observables in the loop representation of the O(n) model at the critical point. We focus on correlation functions containing twist operators, combining these with anchored loops, boundaries with SLE processes and with double SLE processes. We focus further upon n=0, representing self-avoiding loops, which corresponds to a logarithmic conformal field theory (LCFT) with c=0. In this limit the twist operator plays the role of a zero weight indicator operator, which we verify by comparison with known examples. Using the additional conditions imposed by the twist operator null-states, we derive a new explicit result for the probabilities that an SLE_{8/3} wind in various ways about two points in the upper half plane, e.g. that the SLE passes to the left of both points. The collection of c=0 logarithmic CFT operators that we use deriving the winding probabilities is novel, highlighting a potential incompatibility caused by the presence of two distinct logarithmic partners to the stress tensor within the theory. We provide evidence that both partners do appear in the theory, one in the bulk and one on the boundary and that the incompatibility is resolved by restrictive bulk-boundary fusion rules.Comment: 18 pages, 8 figure

    Projections in string theory and boundary states for Gepner models

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    In string theory various projections have to be imposed to ensure supersymmetry. We study the consequences of these projections in the presence of world sheet boundaries. A-type boundary conditions come in several classes; only boundary fields that do not change the class preserve supersymmetry. Our analysis takes in particular properly into account the resolution of fixed points under the projections. Thus e.g. the compositeness of some previously considered boundary states of Gepner models follows from chiral properties of the projections. Our arguments are model independent; in particular, integrality of all annulus coefficients is ensured by model independent arguments.Comment: 37 pages, LaTeX2

    Multiple Schramm-Loewner Evolutions and Statistical Mechanics Martingales

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    A statistical mechanics argument relating partition functions to martingales is used to get a condition under which random geometric processes can describe interfaces in 2d statistical mechanics at criticality. Requiring multiple SLEs to satisfy this condition leads to some natural processes, which we study in this note. We give examples of such multiple SLEs and discuss how a choice of conformal block is related to geometric configuration of the interfaces and what is the physical meaning of mixed conformal blocks. We illustrate the general ideas on concrete computations, with applications to percolation and the Ising model.Comment: 40 pages, 6 figures. V2: well, it looks better with the addresse
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