5,745 research outputs found
On Recurrent Reachability for Continuous Linear Dynamical Systems
The continuous evolution of a wide variety of systems, including
continuous-time Markov chains and linear hybrid automata, can be described in
terms of linear differential equations. In this paper we study the decision
problem of whether the solution of a system of linear
differential equations reaches a target
halfspace infinitely often. This recurrent reachability problem can
equivalently be formulated as the following Infinite Zeros Problem: does a
real-valued function satisfying a
given linear differential equation have infinitely many zeros? Our main
decidability result is that if the differential equation has order at most ,
then the Infinite Zeros Problem is decidable. On the other hand, we show that a
decision procedure for the Infinite Zeros Problem at order (and above)
would entail a major breakthrough in Diophantine Approximation, specifically an
algorithm for computing the Lagrange constants of arbitrary real algebraic
numbers to arbitrary precision.Comment: Full version of paper at LICS'1
Analysis of cubic permutation polynomials for turbo codes
Quadratic permutation polynomials (QPPs) have been widely studied and used as
interleavers in turbo codes. However, less attention has been given to cubic
permutation polynomials (CPPs). This paper proves a theorem which states
sufficient and necessary conditions for a cubic permutation polynomial to be a
null permutation polynomial. The result is used to reduce the search complexity
of CPP interleavers for short lengths (multiples of 8, between 40 and 352), by
improving the distance spectrum over the set of polynomials with the largest
spreading factor. The comparison with QPP interleavers is made in terms of
search complexity and upper bounds of the bit error rate (BER) and frame error
rate (FER) for AWGN and for independent fading Rayleigh channels. Cubic
permutation polynomials leading to better performance than quadratic
permutation polynomials are found for some lengths.Comment: accepted for publication to Wireless Personal Communications (19
pages, 4 figures, 5 tables). The final publication is available at
springerlink.co
Distributional versions of Littlewood's Tauberian theorem
We provide several general versions of Littlewood's Tauberian theorem. These
versions are applicable to Laplace transforms of Schwartz distributions. We
apply these Tauberian results to deduce a number of Tauberian theorems for
power series where Ces\`{a}ro summability follows from Abel summability. We
also use our general results to give a new simple proof of the classical
Littlewood one-sided Tauberian theorem for power series.Comment: 15 page
Gravitational Microlensing Near Caustics I: Folds
We study the local behavior of gravitational lensing near fold catastrophes.
Using a generic form for the lensing map near a fold, we determine the
observable properties of the lensed images, focusing on the case when the
individual images are unresolved, i.e., microlensing. Allowing for images not
associated with the fold, we derive analytic expressions for the photometric
and astrometric behavior near a generic fold caustic. We show how this form
reduces to the more familiar linear caustic, which lenses a nearby source into
two images which have equal magnification, opposite parity, and are equidistant
from the critical curve. In this case, the simplicity and high degree of
symmetry allows for the derivation of semi-analytic expressions for the
photometric and astrometric deviations in the presence of finite sources with
arbitrary surface brightness profiles. We use our results to derive some basic
properties of astrometric microlensing near folds, in particular we predict for
finite sources with uniform and limb darkening profiles, the detailed shape of
the astrometric curve as the source crosses a fold. We find that the
astrometric effects of limb darkening will be difficult to detect with the
currently planned accuracy of the Space Interferometry Mission. We verify our
results by numerically calculating the expected astrometric shift for the
photometrically well-covered Galactic binary lensing event OGLE-1999-BUL-23,
finding excellent agreement with our analytic expressions. Our results can be
applied to any lensing system with fold caustics, including Galactic binary
lenses and quasar microlensing.Comment: 37 pages, 7 figures. Revised version includes an expanded discussion
of applications. Accepted to ApJ, to appear in the August 1, 2002 issue
(v574
Two types of nematicity in the phase diagram of the cuprate superconductor YBaCuO
Nematicity has emerged as a key feature of cuprate superconductors, but its
link to other fundamental properties such as superconductivity, charge order
and the pseudogap remains unclear. Here we use measurements of transport
anisotropy in YBaCuO to distinguish two types of nematicity. The
first is associated with short-range charge-density-wave modulations in a
doping region near . It is detected in the Nernst coefficient, but
not in the resistivity. The second type prevails at lower doping, where there
are spin modulations but no charge modulations. In this case, the onset of
in-plane anisotropy - detected in both the Nernst coefficient and the
resistivity - follows a line in the temperature-doping phase diagram that
tracks the pseudogap energy. We discuss two possible scenarios for the latter
nematicity.Comment: 8 pages and 7 figures. Main text and supplementary material now
combined into single articl
Exact Quantum Solutions of Extraordinary N-body Problems
The wave functions of Boson and Fermion gases are known even when the
particles have harmonic interactions. Here we generalise these results by
solving exactly the N-body Schrodinger equation for potentials V that can be
any function of the sum of the squares of the distances of the particles from
one another in 3 dimensions. For the harmonic case that function is linear in
r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) =
\zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2
M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the
solution is given in terms of the one or two body problem with potential U(r)
in 3 dimensions. The degeneracies of the levels are derived for distinguishable
particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter
involve significant combinatorial analysis which may have application to the
shell model of atomic nuclei. For large N the Fermionic ground state gives the
binding energy of a degenerate white dwarf star treated as a giant atom with an
N-body wave function. The N-body forces involved in these extraordinary N-body
problems are not the usual sums of two body interactions, but nor are forces
between quarks or molecules. Bose-Einstein condensation of particles in 3
dimensions interacting via these strange potentials can be treated by this
method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal
Societ
A measure of majorisation emerging from single-shot statistical mechanics
The use of the von Neumann entropy in formulating the laws of thermodynamics
has recently been challenged. It is associated with the average work whereas
the work guaranteed to be extracted in any single run of an experiment is the
more interesting quantity in general. We show that an expression that
quantifies majorisation determines the optimal guaranteed work. We argue it
should therefore be the central quantity of statistical mechanics, rather than
the von Neumann entropy. In the limit of many identical and independent
subsystems (asymptotic i.i.d) the von Neumann entropy expressions are recovered
but in the non-equilbrium regime the optimal guaranteed work can be radically
different to the optimal average. Moreover our measure of majorisation governs
which evolutions can be realized via thermal interactions, whereas the
nondecrease of the von Neumann entropy is not sufficiently restrictive. Our
results are inspired by single-shot information theory.Comment: 54 pages (15+39), 9 figures. Changed title / changed presentation,
same main results / added minor result on pure bipartite state entanglement
(appendix G) / near to published versio
Retroperitoneal hematoma following hysteroscopic removal of levonorgestrel intrauterine system: a case report
Long acting reversible contraceptive (LARC) devices such as the levonorgestrel intrauterine system (LNG-IUS) have increased in use. Care should be taken with insertion and removal of the device as, although rare, serious complications can occur. We present a case of retroperitoneal hematoma following hysteroscopic removal of LNG-IUS
- …