10,757 research outputs found
On the small-time behavior of subordinators
We prove several results on the behavior near t=0 of for certain
-valued stochastic processes . In particular, we show
for L\'{e}vy subordinators that the Pareto law on is the only
possible weak limit and provide necessary and sufficient conditions for the
convergence. More generally, we also consider the weak convergence of
as for a decreasing function that is slowly varying at zero.
Various examples demonstrating the applicability of the results are presented.Comment: Published in at http://dx.doi.org/10.3150/11-BEJ363 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Tracking the Tracker from its Passive Sonar ML-PDA Estimates
Target motion analysis with wideband passive sonar has received much
attention. Maximum likelihood probabilistic data-association (ML-PDA)
represents an asymptotically efficient estimator for deterministic target
motion, and is especially well-suited for low-observable targets; the results
presented here apply to situations with higher signal to noise ratio as well,
including of course the situation of a deterministic target observed via clean
measurements without false alarms or missed detections. Here we study the
inverse problem, namely, how to identify the observing platform (following a
two-leg motion model) from the results of the target estimation process, i.e.
the estimated target state and the Fisher information matrix, quantities we
assume an eavesdropper might intercept. We tackle the problem and we present
observability properties, with supporting simulation results.Comment: To appear in IEEE Transactions on Aerospace and Electronic System
Quantum random walks without walking
Quantum random walks have received much interest due to their non-intuitive
dynamics, which may hold the key to a new generation of quantum algorithms.
What remains a major challenge is a physical realization that is experimentally
viable and not limited to special connectivity criteria. We present a scheme
for walking on arbitrarily complex graphs, which can be realized using a
variety of quantum systems such as a BEC trapped inside an optical lattice.
This scheme is particularly elegant since the walker is not required to
physically step between the nodes; only flipping coins is sufficient.Comment: 12 manuscript pages, 3 figure
Conflict-Free Coloring Made Stronger
In FOCS 2002, Even et al. showed that any set of discs in the plane can
be Conflict-Free colored with a total of at most colors. That is,
it can be colored with colors such that for any (covered) point
there is some disc whose color is distinct from all other colors of discs
containing . They also showed that this bound is asymptotically tight. In
this paper we prove the following stronger results:
\begin{enumerate} \item [(i)] Any set of discs in the plane can be
colored with a total of at most colors such that (a) for any
point that is covered by at least discs, there are at least
distinct discs each of which is colored by a color distinct from all other
discs containing and (b) for any point covered by at most discs,
all discs covering are colored distinctively. We call such a coloring a
{\em -Strong Conflict-Free} coloring. We extend this result to pseudo-discs
and arbitrary regions with linear union-complexity.
\item [(ii)] More generally, for families of simple closed Jordan regions
with union-complexity bounded by , we prove that there exists
a -Strong Conflict-Free coloring with at most colors.
\item [(iii)] We prove that any set of axis-parallel rectangles can be
-Strong Conflict-Free colored with at most colors.
\item [(iv)] We provide a general framework for -Strong Conflict-Free
coloring arbitrary hypergraphs. This framework relates the notion of -Strong
Conflict-Free coloring and the recently studied notion of -colorful
coloring. \end{enumerate}
All of our proofs are constructive. That is, there exist polynomial time
algorithms for computing such colorings
Computing by nowhere increasing complexity
A cellular automaton is presented whose governing rule is that the Kolmogorov
complexity of a cell's neighborhood may not increase when the cell's present
value is substituted for its future value. Using an approximation of this
two-dimensional Kolmogorov complexity the underlying automaton is shown to be
capable of simulating logic circuits. It is also shown to capture trianry logic
described by a quandle, a non-associative algebraic structure. A similar
automaton whose rule permits at times the increase of a cell's neighborhood
complexity is shown to produce animated entities which can be used as
information carriers akin to gliders in Conway's game of life
High-power 1.3 µm superluminescent diode
Superluminescent diodes with high output power (10 mW at 175 mA), wide spectral width (28 nm), low spectral modulation depth (<15%), wide frequency modulation bandwidth (570 MHz), and high single-mode fiber coupling efficiency (40%) are reported. The structure is based on a buried crescent laser structure with an antireflection coating and a "short-circuit" absorber to suppress lasing
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