10,037 research outputs found
Error correcting code using tree-like multilayer perceptron
An error correcting code using a tree-like multilayer perceptron is proposed.
An original message \mbi{s}^0 is encoded into a codeword \boldmath{y}_0
using a tree-like committee machine (committee tree) or a tree-like parity
machine (parity tree). Based on these architectures, several schemes featuring
monotonic or non-monotonic units are introduced. The codeword \mbi{y}_0 is
then transmitted via a Binary Asymmetric Channel (BAC) where it is corrupted by
noise. The analytical performance of these schemes is investigated using the
replica method of statistical mechanics. Under some specific conditions, some
of the proposed schemes are shown to saturate the Shannon bound at the infinite
codeword length limit. The influence of the monotonicity of the units on the
performance is also discussed.Comment: 23 pages, 3 figures, Content has been extended and revise
Nonlinear force-free field modelling of solar coronal jets in theoretical configurations
Coronal jets occur frequently on the Sun, and may contribute significantly to the solar wind. With the suite of instruments available now, we can observe these phenomena in greater detail than ever before. Modeling and simulations can assist further in understanding the dynamic processes involved, but previous studies tend to consider only one mechanism (e.g. emergence or rotation) for the origin of the jet. In this study we model a series of idealised archetypal jet configurations and follow the evolution of the coronal magnetic field. This is a step towards understanding these idealised situations before considering their observational counterparts. Several simple situations are set up for the evolution of the photospheric magnetic field: a single parasitic polarity rotating or moving in a circular path; as well as opposite polarity pairs involved in flyby (shearing), cancellation or emergence; all in the presence of a uniform, open background magnetic field. The coronal magnetic field is evolved in time using a magnetofrictional relaxation method. While magnetofriction cannot accurately reproduce the dynamics of an eruptive phase, the structure of the coronal magnetic field, as well as the build up of electric currents and free magnetic energy are instructive. Certain configurations and motions produce a flux rope and allow the significant build up of free energy, reminiscent of the progenitors of so-called blowout jets, whereas other, simpler configurations are more comparable to the standard jet model. The next stage is a comparison with observed coronal jet structures and their corresponding photospheric evolution
Stellar Differential Rotation and Coronal Timescales
We investigate the timescales of evolution of stellar coronae in response to
surface differential rotation and diffusion. To quantify this we study both the
formation time and lifetime of a magnetic flux rope in a decaying bipolar
active region. We apply a magnetic flux transport model to prescribe the
evolution of the stellar photospheric field, and use this to drive the
evolution of the coronal magnetic field via a magnetofrictional technique.
Increasing the differential rotation (i.e. decreasing the equator-pole lap
time) decreases the flux rope formation time. We find that the formation time
is dependent upon the geometric mean of the lap time and the surface diffusion
timescale. In contrast, the lifetime of flux ropes are proportional to the lap
time. With this, flux ropes on stars with a differential rotation of more than
eight times the solar value have a lifetime of less than two days. As a
consequence, we propose that features such as solar-like quiescent prominences
may not be easily observable on such stars, as the lifetimes of the flux ropes
which host the cool plasma are very short. We conclude that such high
differential rotation stars may have very dynamical coronae
Cost-effectiveness analysis in R using a multi-state modelling survival analysis framework: a tutorial
This tutorial provides a step-by-step guide to performing cost-effectiveness analysis using a multi-state modelling approach. Alongside the tutorial we provide easy-to-use functions in the statistics package R. We argue this multi-state modelling approach using a package such as R has advantages over approaches where models are built in a spreadsheet package. In particular, using a syntax-based approach means there is a written record of what was done and the calculations are transparent. Reproducing the analysis is straightforward as the syntax just needs to be run again. The approach can be thought of as an alternative way to build a Markov decision analytic model, which also has the option to use a state-arrival extended approach if the Markov property does not hold. In the state-arrival extended multi-state model a covariate that represents patients’ history is included allowing the Markov property to be tested. We illustrate the building of multi-state survival models, making predictions from the models and assessing fits. We then proceed to perform a cost-effectiveness analysis including deterministic and probabilistic sensitivity analyses. Finally, we show how to create two common methods of visualising the results, namely cost-effectiveness planes and cost-effectiveness acceptability curves. The analysis is implemented entirely within R. It is based on adaptions to functions in the existing R package mstate, to accommodate parametric multi-state modelling which facilitates extrapolation of survival curves
Electronic structure of periodic curved surfaces -- topological band structure
Electronic band structure for electrons bound on periodic minimal surfaces is
differential-geometrically formulated and numerically calculated. We focus on
minimal surfaces because they are not only mathematically elegant (with the
surface characterized completely in terms of "navels") but represent the
topology of real systems such as zeolites and negative-curvature fullerene. The
band structure turns out to be primarily determined by the topology of the
surface, i.e., how the wavefunction interferes on a multiply-connected surface,
so that the bands are little affected by the way in which we confine the
electrons on the surface (thin-slab limit or zero thickness from the outset).
Another curiosity is that different minimal surfaces connected by the Bonnet
transformation (such as Schwarz's P- and D-surfaces) possess one-to-one
correspondence in their band energies at Brillouin zone boundaries.Comment: 6 pages, 8 figures, eps files will be sent on request to
[email protected]
Modelling the sun's small scale global photospheric magnetic field
We present a new model for the Sun's global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of small- scale magnetic features across the full solar surface is simulated, subject to the influence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms, to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between small-scale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2:5 Rʘ, around 10 - 100 times less than that determined for typical HMI synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is presently observed, and hence a much higher cosmic ray flux at Earth
Kramers-Kronig, Bode, and the meaning of zero
The implications of causality, as captured by the Kramers-Kronig relations
between the real and imaginary parts of a linear response function, are
familiar parts of the physics curriculum. In 1937, Bode derived a similar
relation between the magnitude (response gain) and phase. Although the
Kramers-Kronig relations are an equality, Bode's relation is effectively an
inequality. This perhaps-surprising difference is explained using elementary
examples and ultimately traces back to delays in the flow of information within
the system formed by the physical object and measurement apparatus.Comment: 8 pages; American Journal of Physics, to appea
A Renormalization Group for Hamiltonians: Numerical Results
We describe a renormalization group transformation that is related to the
breakup of golden invariant tori in Hamiltonian systems with two degrees of
freedom. This transformation applies to a large class of Hamiltonians, is
conceptually simple, and allows for accurate numerical computations. In a
numerical implementation, we find a nontrivial fixed point and determine the
corresponding critical index and scaling. Our computed values for various
universal constants are in good agreement with existing data for
area-preserving maps. We also discuss the flow associated with the nontrivial
fixed point.Comment: 11 Pages, 2 Figures. For future updates, check
ftp://ftp.ma.utexas.edu/pub/papers/koch
Developing Interventions for Children's Exercise (DICE): a pilot evaluation of school-based exercise interventions for primary school children aged 7 to 8 years.
BACKGROUND: Developing Interventions for Children's Exercise (DICE) is an initiative aimed at determining effective school-based exercise programs. To assess feasibility, we conducted a pilot study of exercise sessions which varied in duration and frequency. METHODS: Exercise interventions were delivered to Year 3 pupils (age 7-8 years; n = 73) in primary schools within Yorkshire, UK. Evaluations were conducted using focus group sessions, questionnaires and observations. RESULTS: The study revealed positive aspects of all interventions, including favorable effects on children's concentration during lessons and identified the value of incorporation of the DICE concept into curriculum lessons. Children appeared enthused and reported well-being and enjoyment. Areas requiring attention were the need for appropriate timetabling of sessions and ensuring the availability of space. CONCLUSION: The concept and sessions were well-accepted by teachers who confirmed their full support of any future implementation There appears to be potential for the encouragement and empowerment of teachers to support physical activity and healthy school environments, and to take an interest in the health of their pupils. Ultimately, these findings should assist in the design of successful exercise interventions in the school setting
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