35,380 research outputs found
A Simple Approach to Maximum Intractable Likelihood Estimation
Approximate Bayesian Computation (ABC) can be viewed as an analytic
approximation of an intractable likelihood coupled with an elementary
simulation step. Such a view, combined with a suitable instrumental prior
distribution permits maximum-likelihood (or maximum-a-posteriori) inference to
be conducted, approximately, using essentially the same techniques. An
elementary approach to this problem which simply obtains a nonparametric
approximation of the likelihood surface which is then used as a smooth proxy
for the likelihood in a subsequent maximisation step is developed here and the
convergence of this class of algorithms is characterised theoretically. The use
of non-sufficient summary statistics in this context is considered. Applying
the proposed method to four problems demonstrates good performance. The
proposed approach provides an alternative for approximating the maximum
likelihood estimator (MLE) in complex scenarios
Multiple zero modes of the Dirac operator in three dimensions
One of the key properties of Dirac operators is the possibility of a
degeneracy of zero modes. For the Abelian Dirac operator in three dimensions
the construction of multiple zero modes has been sucessfully carried out only
very recently. Here we generalise these results by discussing a much wider
class of Dirac operators together with their zero modes. Further we show that
those Dirac operators that do admit zero modes may be related to Hopf maps,
where the Hopf index is related to the number of zero modes in a simple way.Comment: Latex file, 20 pages, no figure
A comprehensive treatment of electromagnetic interactions and the three-body spectator equations
We present a general derivation the three-body spectator (Gross) equations
and the corresponding electromagnetic currents. As in previous paper on
two-body systems, the wave equations and currents are derived from those for
Bethe-Salpeter equation with the help of algebraic method using a concise
matrix notation. The three-body interactions and currents introduced by the
transition to the spectator approach are isolated and the matrix elements of
the e.m. current are presented in detail for system of three indistinguishable
particles, namely for elastic scattering and for two and three body break-up.
The general expressions are reduced to the one-boson-exchange approximation to
make contact with previous work. The method is general in that it does not rely
on introduction of the electromagnetic interaction with the help of the minimal
replacement. It would therefore work also for other external fields
Second-order operators with degenerate coefficients
We consider properties of second-order operators on \Ri^d with bounded real symmetric
measurable coefficients. We assume that almost
everywhere, but allow for the possibility that is singular. We associate
with a canonical self-adjoint viscosity operator and examine
properties of the viscosity semigroup generated by . The
semigroup extends to a positive contraction semigroup on the -spaces with
. We establish that it conserves probability, satisfies
~off-diagonal bounds and that the wave equation associated with has
finite speed of propagation. Nevertheless is not always strictly
positive because separation of the system can occur even for subelliptic
operators. This demonstrates that subelliptic semigroups are not ergodic in
general and their kernels are neither strictly positive nor H\"older
continuous. In particular one can construct examples for which both upper and
lower Gaussian bounds fail even with coefficients in C^{2-\varepsilon}(\Ri^d)
with .Comment: 44 page
Diffusive behavior of a greedy traveling salesman
Using Monte Carlo simulations we examine the diffusive properties of the
greedy algorithm in the d-dimensional traveling salesman problem. Our results
show that for d=3 and 4 the average squared distance from the origin is
proportional to the number of steps t. In the d=2 case such a scaling is
modified with some logarithmic corrections, which might suggest that d=2 is the
critical dimension of the problem. The distribution of lengths also shows
marked differences between d=2 and d>2 versions. A simple strategy adopted by
the salesman might resemble strategies chosen by some foraging and hunting
animals, for which anomalous diffusive behavior has recently been reported and
interpreted in terms of Levy flights. Our results suggest that broad and
Levy-like distributions in such systems might appear due to dimension-dependent
properties of a search space.Comment: accepted in Phys. Rev.
SDSS J080531.84+481233.0: An Unresolved L Dwarf/T Dwarf Binary
SDSS J080531.84+481233.0 is a peculiar L-type dwarf that exhibits unusually
blue near-infrared and mid-infrared colors and divergent optical (L4) and
near-infrared (L9.5) spectral classifications. These peculiar spectral traits
have been variously attributed to condensate cloud effects or subsolar
metallicity. Here I present an improved near-infrared spectrum of this source
which further demonstrates the presence of weak CH4 absorption at 1.6 micron
but no corresponding band at 2.2 micron. It is shown that these features can be
collectively reproduced by the combined light spectrum of a binary with L4.5
and T5 components, as deduced by spectral template matching. Thus, SDSS
J080531.84+481233.0 appears to be a new low-mass binary straddling the L
dwarf/T dwarf transition, an evolutionary phase for brown dwarfs that remains
poorly understood by current theoretical models. The case of SDSS
J080531.84+481233.0 further illustrates how a select range of L dwarf/T dwarf
binaries could be identified and characterized without the need for high
angular resolution imaging or radial velocity monitoring, potentially
alleviating some of the detection biases and limitations inherent to such
techniques.Comment: 11 pages, 4 figures, accepted by A
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