1,266 research outputs found
Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
The analytic structure of scattering amplitudes is restricted by Steinmann
relations, which enforce the vanishing of certain discontinuities of
discontinuities. We show that these relations dramatically simplify the
function space for the hexagon function bootstrap in planar maximally
supersymmetric Yang-Mills theory. Armed with this simplification, along with
the constraints of dual conformal symmetry and Regge exponentiation, we obtain
the complete five-loop six-particle amplitude.Comment: 5 pages, 2 figures, 1 impressive table, and 2 ancillary files. v2: a
few clarifications and references added; version to appear in PR
The Double Pentaladder Integral to All Orders
We compute dual-conformally invariant ladder integrals that are capped off by
pentagons at each end of the ladder. Such integrals appear in six-point
amplitudes in planar N=4 super-Yang-Mills theory. We provide exact,
finite-coupling formulas for the basic double pentaladder integrals as a single
Mellin integral over hypergeometric functions. For particular choices of the
dual conformal cross ratios, we can evaluate the integral at weak coupling to
high loop orders in terms of multiple polylogarithms. We argue that the
integrals are exponentially suppressed at strong coupling. We describe the
space of functions that contains all such double pentaladder integrals and
their derivatives, or coproducts. This space, a prototype for the space of
Steinmann hexagon functions, has a simple algebraic structure, which we
elucidate by considering a particular discontinuity of the functions that
localizes the Mellin integral and collapses the relevant symbol alphabet. This
function space is endowed with a coaction, both perturbatively and at finite
coupling, which mixes the independent solutions of the hypergeometric
differential equation and constructively realizes a coaction principle of the
type believed to hold in the full Steinmann hexagon function space.Comment: 70 pages, 3 figures, 4 tables; v2, minor typo corrections and
clarification
Intonation in unaccompanied singing: Accuracy, drift, and a model of reference pitch memory
Copyright 2014 Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America.
The following article appeared in J. Acoust. Soc. Am. 136, 401 (2014) and may be found at http://dx.doi.org/10.1121/1.4881915
The Steinmann Cluster Bootstrap for N=4 Super Yang-Mills Amplitudes
We review the bootstrap method for constructing six- and seven-particle
amplitudes in planar super Yang-Mills theory, by exploiting
their analytic structure. We focus on two recently discovered properties which
greatly simplify this construction at symbol and function level, respectively:
the extended Steinmann relations, or equivalently cluster adjacency, and the
coaction principle. We then demonstrate their power in determining the
six-particle amplitude through six and seven loops in the NMHV and MHV sectors
respectively, as well as the symbol of the NMHV seven-particle amplitude to
four loops.Comment: 36 pages, 4 figures, 5 tables, 1 ancillary file. Contribution to the
proceedings of the Corfu Summer Institute 2019 "School and Workshops on
Elementary Particle Physics and Gravity" (CORFU2019), 31 August - 25
September 2019, Corfu, Greec
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Improving music genre classification using automatically induced harmony rules
We present a new genre classification framework using both low-level signal-based features and high-level harmony features. A state-of-the-art statistical genre classifier based on timbral features is extended using a first-order random forest containing for each genre rules derived from harmony or chord sequences. This random forest has been automatically induced, using the first-order logic induction algorithm TILDE, from a dataset, in which for each chord the degree and chord category are identified, and covering classical, jazz and pop genre classes. The audio descriptor-based genre classifier contains 206 features, covering spectral, temporal, energy, and pitch characteristics of the audio signal. The fusion of the harmony-based classifier with the extracted feature vectors is tested on three-genre subsets of the GTZAN and ISMIR04 datasets, which contain 300 and 448 recordings, respectively. Machine learning classifiers were tested using 5 Ă 5-fold cross-validation and feature selection. Results indicate that the proposed harmony-based rules combined with the timbral descriptor-based genre classification system lead to improved genre classification rates
Deriving health state utilities for the numerical pain rating scale
Background
The use of patient reported outcome measures within cost-effectiveness analysis has become commonplace. However, specific measures are required that produce values, referred to as 'utilities', that are capable of generating quality adjusted life years. One such measure - the EQ-5D - has come under criticism due to the inherent limitations of its three-level response scales. In evaluations of chronic pain, the numerical pain rating scale (NPRS) which has eleven levels is routinely used which has a greater measurement range, but which can not be used in cost-effetiveness analyses. This study derived utility values for a series of EQ-5D health states that replace the pain dimensions with the NPRS, thereby allowing a potentially greater range of pain intensities to be captured and included in economic analyses.
Methods
Interviews were undertaken with 100 member of the general population. Health state valuations were elicited using the time trade-off approach with a ten year time horizon. Additionally, respondents were asked where the EQ-5D response scale descriptors of moderate and extreme pain lay on the 11-point NPRS scale.
Results
625 valuations were undertaken across the study sample with the crude mean health state utilities showing a negative non-linear relationship with respect to increasing pain intensity. Relative to a NPRS of zero (NPRS0), the successive pain levels (NPRS1-10) had mean decrements in utility of 0.034, 0.043, 0.061, 0.121, 0.144, 0.252, 0.404, 0.575, 0.771 and 0.793, respectively. When respondents were asked to mark on the NPRS scale the EQ-5D pain descriptors of moderate and extreme pain, the median responses were '4' and '8', respectively.
Conclusions
These results demonstrate the potential floor effect of the EQ-5D with respect to pain and provide estimates of health reduction associated with pain intensity described by the NPRS. These estimates are in excess of the decrements produced by an application of the EQ-5D scoring tariff for both the United States and the United Kingdom
Six-Gluon Amplitudes in Planar Super-Yang-Mills Theory at Six and Seven Loops
We compute the six-particle maximally-helicity-violating (MHV) and
next-to-MHV (NMHV) amplitudes in planar maximally supersymmetric Yang-Mills
theory through seven loops and six loops, respectively, as an application of
the extended Steinmann relations and using the cosmic Galois coaction
principle. Starting from a minimal space of functions constructed using these
principles, we identify the amplitude by matching its symmetries and predicted
behavior in various kinematic limits. Through five loops, the MHV and NMHV
amplitudes are uniquely determined using only the multi-Regge and leading
collinear limits. Beyond five loops, the MHV amplitude requires additional data
from the kinematic expansion around the collinear limit, which we obtain from
the Pentagon Operator Product Expansion, and in particular from its
single-gluon bound state contribution. We study the MHV amplitude in the
self-crossing limit, where its singular terms agree with previous predictions.
Analyzing and plotting the amplitudes along various kinematical lines, we
continue to find remarkable stability between loop orders.Comment: 51 pages, 9 figures, 1 table; v2: minor typo corrections, version to
appear in JHE
The environmental security debate and its significance for climate change
Policymakers, military strategists and academics all increasingly hail climate change as a security issue. This article revisits the (comparatively) long-standing âenvironmental security debateâ and asks what lessons that earlier debate holds for the push towards making climate change a security issue. Two important claims are made. First, the emerging climate security debate is in many ways a re-run of the earlier dispute. It features many of the same proponents and many of the same disagreements. These disagreements concern, amongst other things, the nature of the threat, the referent object of security and the appropriate policy responses. Second, given its many different interpretations, from an environmentalist perspective, securitisation of the climate is not necessarily a positive development
A Zoomable Mapping of a Musical Parameter Space Using Hilbert Curves
The final publication is available at Computer Music Journal via http://dx.doi.org/10.1162/COMJ_a_0025
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