26 research outputs found
Measurement as Absorption of Feynman Trajectories: Collapse of the Wave Function Can be Avoided
We define a measuring device (detector) of the coordinate of quantum particle
as an absorbing wall that cuts off the particle's wave function. The wave
function in the presence of such detector vanishes on the detector. The trace
the absorbed particles leave on the detector is identifies as the absorption
current density on the detector. This density is calculated from the solution
of Schr\"odinger's equation with a reflecting boundary at the detector. This
current density is not the usual Schr\"odinger current density. We define the
probability distribution of the time of arrival to a detector in terms of the
absorption current density. We define coordinate measurement by an absorbing
wall in terms of 4 postulates. We postulate, among others, that a quantum
particle has a trajectory. In the resulting theory the quantum mechanical
collapse of the wave function is replaced with the usual collapse of the
probability distribution after observation. Two examples are presented, that of
the slit experiment and the slit experiment with absorbing boundaries to
measure time of arrival. A calculation is given of the two dimensional
probability density function of a free particle from the measurement of the
absorption current on two planes.Comment: 20 pages, latex, no figure
Genetic attack on neural cryptography
Different scaling properties for the complexity of bidirectional
synchronization and unidirectional learning are essential for the security of
neural cryptography. Incrementing the synaptic depth of the networks increases
the synchronization time only polynomially, but the success of the geometric
attack is reduced exponentially and it clearly fails in the limit of infinite
synaptic depth. This method is improved by adding a genetic algorithm, which
selects the fittest neural networks. The probability of a successful genetic
attack is calculated for different model parameters using numerical
simulations. The results show that scaling laws observed in the case of other
attacks hold for the improved algorithm, too. The number of networks needed for
an effective attack grows exponentially with increasing synaptic depth. In
addition, finite-size effects caused by Hebbian and anti-Hebbian learning are
analyzed. These learning rules converge to the random walk rule if the synaptic
depth is small compared to the square root of the system size.Comment: 8 pages, 12 figures; section 5 amended, typos correcte
A Scaling Theory of Bifurcations in the Symmetric Weak-Noise Escape Problem
We consider the overdamped limit of two-dimensional double well systems
perturbed by weak noise. In the weak noise limit the most probable
fluctuational path leading from either point attractor to the separatrix (the
most probable escape path, or MPEP) must terminate on the saddle between the
two wells. However, as the parameters of a symmetric double well system are
varied, a unique MPEP may bifurcate into two equally likely MPEP's. At the
bifurcation point in parameter space, the activation kinetics of the system
become non-Arrhenius. In this paper we quantify the non-Arrhenius behavior of a
system at the bifurcation point, by using the Maslov-WKB method to construct an
approximation to the quasistationary probability distribution of the system
that is valid in a boundary layer near the separatrix. The approximation is a
formal asymptotic solution of the Smoluchowski equation. Our analysis relies on
the development of a new scaling theory, which yields `critical exponents'
describing weak-noise behavior near the saddle, at the bifurcation point.Comment: LaTeX, 60 pages, 24 Postscript figures. Uses epsf macros to include
the figures. A file in `uufiles' format containing the figures is separately
available at ftp://platinum.math.arizona.edu/pub/papers-rsm/paperF/figures.uu
and a Postscript version of the whole paper (figures included) is available
at ftp://platinum.math.arizona.edu/pub/papers-rsm/paperF/paperF.p
The Escape Problem for Irreversible Systems
The problem of noise-induced escape from a metastable state arises in
physics, chemistry, biology, systems engineering, and other areas. The problem
is well understood when the underlying dynamics of the system obey detailed
balance. When this assumption fails many of the results of classical
transition-rate theory no longer apply, and no general method exists for
computing the weak-noise asymptotics of fundamental quantities such as the mean
escape time. In this paper we present a general technique for analysing the
weak-noise limit of a wide range of stochastically perturbed continuous-time
nonlinear dynamical systems. We simplify the original problem, which involves
solving a partial differential equation, into one in which only ordinary
differential equations need be solved. This allows us to resolve some old
issues for the case when detailed balance holds. When it does not hold, we show
how the formula for the mean escape time asymptotics depends on the dynamics of
the system along the most probable escape path. We also present new results on
short-time behavior and discuss the possibility of focusing along the escape
path.Comment: 24 pages, APS revtex macros (version 2.1) now available from PBB via
`get oldrevtex.sty
âProclaim Liberty Throughout All the Land unto All the Inhabitants Thereof!â:Reading Leviticus 25:10 Through the Centuries
Y-chromosome R-M343 African lineages and sickle cell disease reveal structured assimilation in Lebanon
We have sought to identify signals of assimilation of African male lines in Lebanon by exploring the association of sickle cell disease in Lebanon with Y-chromosome haplogroups that are informative of the disease origin and its exclusivity to the Muslim community. A total of 732 samples were analyzed including 33 sickle cell disease patients from Lebanon genotyped for 28 binary markers and 19 short tandem repeats on the non-recombinant segment of the Y chromosome. Genetic organization was identified using populations known to have influenced the genetic structure of the Lebanese population, in addition to African populations with high incidence of sickle cell disease. Y-chromosome haplogroup R-M343 sub-lineages distinguish between sub-Saharan African and Lebanese Y chromosomes. We detected a limited penetration of sickle cell disease into Lebanese R-M343 carriers, restricted to Lebanese Muslims. We suggest that this penetration brought the sickle cell gene along with the African R-M343, probably with the Saharan caravan slave trade