30,049 research outputs found
Intrinsic Variability and Field Statistics for the Vela Pulsar: 3. Two-Component Fits and Detailed Assessment of Stochastic Growth Theory
The variability of the Vela pulsar (PSR B0833-45) corresponds to well-defined
field statistics that vary with pulsar phase, ranging from Gaussian intensity
statistics off-pulse to approximately power-law statistics in a transition
region and then lognormal statistics on-pulse, excluding giant micropulses.
These data are analyzed here in terms of two superposed wave populations, using
a new calculation for the amplitude statistics of two vectorially-combined
transverse fields. Detailed analyses show that the approximately power-law and
lognormal distributions observed are fitted well at essentially all on-pulse
phases by Gaussian-lognormal and double-lognormal combinations, respectively.
These good fits, plus the smooth but significant variations in fit parameters
across the source, provide strong evidence that the approximately power-law
statistics observed in the transition region are not intrinsic. Instead, the
data are consistent with normal pulsar emission having lognormal statistics at
all phases. This is consistent with generation in an inhomogeneous source
obeying stochastic growth theory (SGT) and with the emission mechanism being
purely linear (either direct or indirect). A nonlinear mechanism is viable only
if it produces lognormal statistics when suitably ensemble-averaged. Variations
in the SGT fit parameters with phase imply that the radiation is relatively
more variable near the pulse edges than near the center, as found in earlier
work. In contrast, Vela's giant micropulses come from a very restricted phase
range and have power-law statistics with indices () not
inconsistent with nonlinear wave collapse. These results imply that normal
pulses have a different source and generation mechanism than giant micropulses,
as suggested previously on other grounds.Comment: 10 pages and 14 figures. Accepted by Monthly Notices of the Royal
Astronomical Society in April 200
A second derivative SQP method: theoretical issues
Sequential quadratic programming (SQP) methods form a class of highly efficient algorithms for solving nonlinearly constrained optimization problems. Although second derivative information may often be calculated, there is little practical theory that justifies exact-Hessian SQP methods. In particular, the resulting quadratic programming (QP) subproblems are often nonconvex, and thus finding their global solutions may be computationally nonviable. This paper presents a second-derivative SQP method based on quadratic subproblems that are either convex, and thus may be solved efficiently, or need not be solved globally. Additionally, an explicit descent-constraint is imposed on certain QP subproblems, which âguidesâ the iterates through areas in which nonconvexity is a concern. Global convergence of the resulting algorithm is established
Intrinsic Variability and Field Statistics for the Vela Pulsar: 2. Systematics and Single-Component Fits
Individual pulses from pulsars have intensity-phase profiles that differ
widely from pulse to pulse, from the average profile, and from phase to phase
within a pulse. Widely accepted explanations do not exist for this variability
or for the mechanism producing the radiation. The variability corresponds to
the field statistics, particularly the distribution of wave field amplitudes,
which are predicted by theories for wave growth in inhomogeneous media. This
paper shows that the field statistics of the Vela pulsar (PSR B0833-45) are
well-defined and vary as a function of pulse phase, evolving from Gaussian
intensity statistics off-pulse to approximately power-law and then lognormal
distributions near the pulse peak to approximately power-law and eventually
Gaussian statistics off-pulse again. Detailed single-component fits confirm
that the variability corresponds to lognormal statistics near the peak of the
pulse profile and Gaussian intensity statistics off-pulse. The lognormal field
statistics observed are consistent with the prediction of stochastic growth
theory (SGT) for a purely linear system close to marginal stability. The
simplest interpretations are that the pulsar's variability is a direct
manifestation of an SGT state and the emission mechanism is linear (either
direct or indirect), with no evidence for nonlinear mechanisms like
modulational instability and wave collapse which produce power-law field
statistics. Stringent constraints are placed on nonlinear mechanisms: they must
produce lognormal statistics when suitably ensemble-averaged. Field statistics
are thus a powerful, potentially widely applicable tool for understanding
variability and constraining mechanisms and source characteristics of coherent
astrophysical and space emissions.Comment: 11 pages, 12 figures. Accepted by Monthly Notices of the Royal
Astronmical Society in April 200
A second derivative SQP method: local convergence
In [19], we gave global convergence results for a second-derivative SQP method for minimizing the exact â1-merit function for a fixed value of the penalty parameter. To establish this result, we used the properties of the so-called Cauchy step, which was itself computed from the so-called predictor step. In addition, we allowed for the computation of a variety of (optional) SQP steps that were intended to improve the efficiency of the algorithm. \ud
\ud
Although we established global convergence of the algorithm, we did not discuss certain aspects that are critical when developing software capable of solving general optimization problems. In particular, we must have strategies for updating the penalty parameter and better techniques for defining the positive-definite matrix Bk used in computing the predictor step. In this paper we address both of these issues. We consider two techniques for defining the positive-definite matrix Bkâa simple diagonal approximation and a more sophisticated limited-memory BFGS update. We also analyze a strategy for updating the penalty paramter based on approximately minimizing the â1-penalty function over a sequence of increasing values of the penalty parameter.\ud
\ud
Algorithms based on exact penalty functions have certain desirable properties. To be practical, however, these algorithms must be guaranteed to avoid the so-called Maratos effect. We show that a nonmonotone varient of our algorithm avoids this phenomenon and, therefore, results in asymptotically superlinear local convergence; this is verified by preliminary numerical results on the Hock and Shittkowski test set
A second-derivative trust-region SQP method with a "trust-region-free" predictor step
In (NAR 08/18 and 08/21, Oxford University Computing Laboratory, 2008) we introduced a second-derivative SQP method (S2QP) for solving nonlinear nonconvex optimization problems. We proved that the method is globally convergent and locally superlinearly convergent under standard assumptions. A critical component of the algorithm is the so-called predictor step, which is computed from a strictly convex quadratic program with a trust-region constraint. This step is essential for proving global convergence, but its propensity to identify the optimal active set is Paramount for recovering fast local convergence. Thus the global and local efficiency of the method is intimately coupled with the quality of the predictor step.\ud
\ud
In this paper we study the effects of removing the trust-region constraint from the computation of the predictor step; this is reasonable since the resulting problem is still strictly convex and thus well-defined. Although this is an interesting theoretical question, our motivation is based on practicality. Our preliminary numerical experience with S2QP indicates that the trust-region constraint occasionally degrades the quality of the predictor step and diminishes its ability to correctly identify the optimal active set. Moreover, removal of the trust-region constraint allows for re-use of the predictor step over a sequence of failed iterations thus reducing computation. We show that the modified algorithm remains globally convergent and preserves local superlinear convergence provided a nonmonotone strategy is incorporated
Shear-Free Gravitational Waves in an Anisotropic Universe
We study gravitational waves propagating through an anisotropic Bianchi I
dust-filled universe (containing the Einstein-de-Sitter universe as a special
case). The waves are modeled as small perturbations of this background
cosmological model and we choose a family of null hypersurfaces in this
space-time to act as the histories of the wavefronts of the radiation. We find
that the perturbations we generate can describe pure gravitational radiation if
and only if the null hypersurfaces are shear-free. We calculate the
gauge-invariant small perturbations explicitly in this case. How these differ
from the corresponding perturbations when the background space-time is
isotropic is clearly exhibited.Comment: 32 pages, accepted for publication in Physical Review
On solving trust-region and other regularised subproblems in optimization
The solution of trust-region and regularisation subproblems which arise in unconstrained optimization is considered. Building on the pioneering work of Gay, MorÂŽe and Sorensen, methods which obtain the solution of a sequence of parametrized linear systems by factorization are used. Enhancements using high-order polynomial approximation and inverse iteration ensure that the resulting method is both globally and asymptotically at least superlinearly convergent in all cases, including in the notorious hard case. Numerical experiments validate the effectiveness of our approach. The resulting software is available as packages TRS and RQS as part of the GALAHAD optimization library, and is especially designed for large-scale problems
"If she had broken her leg she would not have waited in agony for 9 months": Caregiver's experiences of eating disorder treatment
This study aims to explore caregivers' experiences of eating disorder services and subsequent impacts on the caregiving burden and patient outcomes. Thematic analysis was employed to investigate qualitative data from a caregiverâtargeted online survey run by BEAT, the UK's largest eating disorder charity. Six hundred and 16 caregivers completed the survey. Participants' experiences of eating disorder treatment were predominantly negative, characterised by three main themes: (a) Barriers to care: enduring obstacles caregivers face in accessing support for their loved ones, (b) Experiences of services: high levels of unmet needs for caregivers and patients alike, (c) Affected domains: the pervasive impact of caregiving, influenced by experiences of services. This study is the largest of its kind to explore caregivers' experiences of eating disorder treatment services and aims to give voice to this overlooked group within research. Notably, little has been done to address broader systemic challenges faced by caregivers in accessing support for loved ones. Results indicate these challenges may play a substantial role in shaping the caregiving burden, carer coping styles, and subsequent patient outcomes. Findings denote wider systemic issues and a lack of specificities of information and practical skills that could help prevent caregivers from experiencing the caregiving burden and subsequent consequences on eating disorder patient outcomes
- âŠ