1,392 research outputs found
Iterated function systems with a given continuous stationary distribution
For any continuous probability measure on we construct an
IFS with probabilities having as its unique measure-attractor.Comment: 7 pages, 3 figure
Differentiability of fractal curves
While self-similar sets have no tangents at any single point, self-affine
curves can be smooth. We consider plane self-affine curves without double
points and with two pieces. There is an open subset of parameter space for
which the curve is differentiable at all points except for a countable set. For
a parameter set of codimension one, the curve is continuously differentiable.
However, there are no twice differentiable self-affine curves in the plane,
except for parabolic arcs
Hurst Coefficient in long time series of population size: Model for two plant populations with different reproductive strategies
Can the fractal dimension of fluctuations in population size be used to estimate extinction risk? The problem with estimating this fractal dimension is that the lengths of the time series are usually too short for conclusive results. This study answered this question with long time series data obtained from an iterative competition model. This model produces competitive extinction at different perturbation intensities for two different germination strategies: germination of all seeds vs. dormancy in half the seeds. This provided long time series of 900 years and different extinction risks. The results support the hypothesis for the effectiveness of the Hurst coefficient for estimating extinction risk
On the "Mandelbrot set" for a pair of linear maps and complex Bernoulli convolutions
We consider the "Mandelbrot set" for pairs of complex linear maps,
introduced by Barnsley and Harrington in 1985 and studied by Bousch, Bandt and
others. It is defined as the set of parameters in the unit disk such
that the attractor of the IFS is
connected. We show that a non-trivial portion of near the imaginary axis is
contained in the closure of its interior (it is conjectured that all non-real
points of are in the closure of the set of interior points of ). Next we
turn to the attractors themselves and to natural measures
supported on them. These measures are the complex analogs of
much-studied infinite Bernoulli convolutions. Extending the results of Erd\"os
and Garsia, we demonstrate how certain classes of complex algebraic integers
give rise to singular and absolutely continuous measures . Next we
investigate the Hausdorff dimension and measure of , for
in the set , for Lebesgue-a.e. . We also obtain partial results on
the absolute continuity of for a.e. of modulus greater
than .Comment: 22 pages, 5 figure
Poisson-to-Wigner crossover transition in the nearest-neighbor spacing statistics of random points on fractals
We show that the nearest-neighbor spacing distribution for a model that
consists of random points uniformly distributed on a self-similar fractal is
the Brody distribution of random matrix theory. In the usual context of
Hamiltonian systems, the Brody parameter does not have a definite physical
meaning, but in the model considered here, the Brody parameter is actually the
fractal dimension. Exploiting this result, we introduce a new model for a
crossover transition between Poisson and Wigner statistics: random points on a
continuous family of self-similar curves with fractal dimension between 1 and
2. The implications to quantum chaos are discussed, and a connection to
conservative classical chaos is introduced.Comment: Low-resolution figure is included here. Full resolution image
available (upon request) from the author
A differential method for bounding the ground state energy
For a wide class of Hamiltonians, a novel method to obtain lower and upper
bounds for the lowest energy is presented. Unlike perturbative or variational
techniques, this method does not involve the computation of any integral (a
normalisation factor or a matrix element). It just requires the determination
of the absolute minimum and maximum in the whole configuration space of the
local energy associated with a normalisable trial function (the calculation of
the norm is not needed). After a general introduction, the method is applied to
three non-integrable systems: the asymmetric annular billiard, the many-body
spinless Coulombian problem, the hydrogen atom in a constant and uniform
magnetic field. Being more sensitive than the variational methods to any local
perturbation of the trial function, this method can used to systematically
improve the energy bounds with a local skilled analysis; an algorithm relying
on this method can therefore be constructed and an explicit example for a
one-dimensional problem is given.Comment: Accepted for publication in Journal of Physics
Astrophysical thermonuclear functions
As theoretical knowledge and experimental verification of nuclear cross
sections increases it becomes possible to refine analytic representations for
nuclear reaction rates. In this paper mathematical/statistical techniques for
deriving closed-form representations of thermonuclear functions are summarized
and numerical results for them are given.The purpose of the paper is also to
compare numerical results for approximate and closed-form representations of
thermonuclear functions.Comment: 17 pages in LaTeX, 8 figures available on request from
[email protected]
Feedback GAP: pragmatic, cluster-randomized trial of goal setting and action plans to increase the effectiveness of audit and feedback interventions in primary care
Background
Audit and feedback to physicians is a commonly used quality improvement strategy, but its optimal design is unknown. This trial tested the effects of a theory-informed worksheet to facilitate goal setting and action planning, appended to feedback reports on chronic disease management, compared to feedback reports provided without these worksheets.
Methods
A two-arm pragmatic cluster randomized trial was conducted, with allocation at the level of primary care clinics. Participants were family physicians who contributed data from their electronic medical records. The ‘usual feedback’ arm received feedback every six months for two years regarding the proportion of their patients meeting quality targets for diabetes and/or ischemic heart disease. The intervention arm received these same reports plus a worksheet designed to facilitate goal setting and action plan development in response to the feedback reports. Blood pressure (BP) and low-density lipoprotein cholesterol (LDL) values were compared after two years as the primary outcomes. Process outcomes measured the proportion of guideline-recommended actions (e.g., testing and prescribing) conducted within the appropriate timeframe. Intention-to-treat analysis was performed.
Results
Outcomes were similar across groups at baseline. Final analysis included 20 physicians from seven clinics and 1,832 patients in the intervention arm (15% loss to follow up) and 29 physicians from seven clinics and 2,223 patients in the usual feedback arm (10% loss to follow up). Ten of 20 physicians completed the worksheet at least once during the study. Mean BP was 128/72 in the feedback plus worksheet arm and 128/73 in the feedback alone arm, while LDL was 2.1 and 2.0, respectively. Thus, no significant differences were observed across groups in the primary outcomes, but mean haemoglobin A1c was lower in the feedback plus worksheet arm (7.2% versus 7.4%, p<0.001). Improvements in both arms were noted over time for one-half of the process outcomes.
Discussion
Appending a theory-informed goal setting and action planning worksheet to an externally produced audit and feedback intervention did not lead to improvements in patient outcomes. The results may be explained in part by passive dissemination of the worksheet leading to inadequate engagement with the intervention
Irreversibility in a simple reversible model
This paper studies a parametrized family of familiar generalized baker maps,
viewed as simple models of time-reversible evolution. Mapping the unit square
onto itself, the maps are partly contracting and partly expanding, but they
preserve the global measure of the definition domain. They possess periodic
orbits of any period, and all maps of the set have attractors with well defined
structure. The explicit construction of the attractors is described and their
structure is studied in detail. There is a precise sense in which one can speak
about absolute age of a state, regardless of whether the latter is applied to a
single point, a set of points, or a distribution function. One can then view
the whole trajectory as a set of past, present and future states. This
viewpoint is then applied to show that it is impossible to define a priori
states with very large "negative age". Such states can be defined only a
posteriori. This gives precise sense to irreversibility -- or the "arrow of
time" -- in these time-reversible maps, and is suggested as an explanation of
the second law of thermodynamics also for some realistic physical systems.Comment: 15 pages, 12 Postscript figure
Quantum Iterated Function Systems
Iterated functions system (IFS) is defined by specifying a set of functions
in a classical phase space, which act randomly on an initial point. In an
analogous way, we define a quantum iterated functions system (QIFS), where
functions act randomly with prescribed probabilities in the Hilbert space. In a
more general setting a QIFS consists of completely positive maps acting in the
space of density operators. We present exemplary classical IFSs, the invariant
measure of which exhibits fractal structure, and study properties of the
corresponding QIFSs and their invariant states.Comment: 12 pages, 1 figure include
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