7,075 research outputs found
Polarized Protons in HERA
Polarized proton beams at HERA can currently only be produced by extracting a
beam from a polarized source and then accelerating it in the three synchrotrons
at DESY. In this paper, the processes which can depolarize a proton beam in
circular accelerators are explained, devices which could avoid this
depolarization in the DESY accelerator chain are described, and specific
problems which become important at the high energies of HERA are mentioned. At
HERA's high energies, spin motion cannot be accurately described with the
isolated resonance model which has been successfully used for lower energy
rings. To illustrate the principles of more accurate simulations, the invariant
spin field is introduced to describe the equilibrium polarization state of a
beam and the changes during acceleration. It will be shown how linearized spin
motion leads to a computationally quick approximation for the invariant spin
field and how to amend this with more time consuming but accurate
non-perturbative computations. Analysis with these techniques has allowed us to
establish optimal Siberian Snake schemes for HERA
Strength of Higher-Order Spin-Orbit Resonances
When polarized particles are accelerated in a synchrotron, the spin
precession can be periodically driven by Fourier components of the
electromagnetic fields through which the particles travel. This leads to
resonant perturbations when the spin-precession frequency is close to a linear
combination of the orbital frequencies. When such resonance conditions are
crossed, partial depolarization or spin flip can occur. The amount of
polarization that survives after resonance crossing is a function of the
resonance strength and the crossing speed. This function is commonly called the
Froissart-Stora formula. It is very useful for predicting the amount of
polarization after an acceleration cycle of a synchrotron or for computing the
required speed of the acceleration cycle to maintain a required amount of
polarization. However, the resonance strength could in general only be computed
for first-order resonances and for synchrotron sidebands. When Siberian Snakes
adjust the spin tune to be 1/2, as is required for high energy accelerators,
first-order resonances do not appear and higher-order resonances become
dominant. Here we will introduce the strength of a higher-order spin-orbit
resonance, and also present an efficient method of computing it. Several
tracking examples will show that the so computed resonance strength can indeed
be used in the Froissart-Stora formula. HERA-p is used for these examples which
demonstrate that our results are very relevant for existing accelerators.Comment: 10 pages, 6 figure
Discriminative Cooperative Networks for Detecting Phase Transitions
The classification of states of matter and their corresponding phase
transitions is a special kind of machine-learning task, where physical data
allow for the analysis of new algorithms, which have not been considered in the
general computer-science setting so far. Here we introduce an unsupervised
machine-learning scheme for detecting phase transitions with a pair of
discriminative cooperative networks (DCN). In this scheme, a guesser network
and a learner network cooperate to detect phase transitions from fully
unlabeled data. The new scheme is efficient enough for dealing with phase
diagrams in two-dimensional parameter spaces, where we can utilize an active
contour model -- the snake -- from computer vision to host the two networks.
The snake, with a DCN "brain", moves and learns actively in the parameter
space, and locates phase boundaries automatically
A fast Bayesian approach to discrete object detection in astronomical datasets - PowellSnakes I
A new fast Bayesian approach is introduced for the detection of discrete
objects immersed in a diffuse background. This new method, called PowellSnakes,
speeds up traditional Bayesian techniques by: i) replacing the standard form of
the likelihood for the parameters characterizing the discrete objects by an
alternative exact form that is much quicker to evaluate; ii) using a
simultaneous multiple minimization code based on Powell's direction set
algorithm to locate rapidly the local maxima in the posterior; and iii)
deciding whether each located posterior peak corresponds to a real object by
performing a Bayesian model selection using an approximate evidence value based
on a local Gaussian approximation to the peak. The construction of this
Gaussian approximation also provides the covariance matrix of the uncertainties
in the derived parameter values for the object in question. This new approach
provides a speed up in performance by a factor of `hundreds' as compared to
existing Bayesian source extraction methods that use MCMC to explore the
parameter space, such as that presented by Hobson & McLachlan. We illustrate
the capabilities of the method by applying to some simplified toy models.
Furthermore PowellSnakes has the advantage of consistently defining the
threshold for acceptance/rejection based on priors which cannot be said of the
frequentist methods. We present here the first implementation of this technique
(Version-I). Further improvements to this implementation are currently under
investigation and will be published shortly. The application of the method to
realistic simulated Planck observations will be presented in a forthcoming
publication.Comment: 30 pages, 15 figures, revised version with minor changes, accepted
for publication in MNRA
Condorcet domains of tiling type
A Condorcet domain (CD) is a collection of linear orders on a set of
candidates satisfying the following property: for any choice of preferences of
voters from this collection, a simple majority rule does not yield cycles. We
propose a method of constructing "large" CDs by use of rhombus tiling diagrams
and explain that this method unifies several constructions of CDs known
earlier. Finally, we show that three conjectures on the maximal sizes of those
CDs are, in fact, equivalent and provide a counterexample to them.Comment: 16 pages. To appear in Discrete Applied Mathematic
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