68,216 research outputs found
Bayesian outlier detection in Capital Asset Pricing Model
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
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, , the number of lights on each robot, , and
the number of consecutive lights the camera can see, . 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 -cycles in the de Bruijn graph
.
We provide several existence results that give the maximum number of cycles
in in various cases. For example, we give an optimal
solution when . Another construction yields many cycles in larger
de Bruijn graphs using cycles from smaller de Bruijn graphs: if
can be partitioned into -cycles, then
can be partitioned into -cycles for any divisor of
. 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
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
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
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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