53 research outputs found
All Two-Loop MHV Amplitudes in Multi-Regge Kinematics From Applied Symbology
Recent progress on scattering amplitudes has benefited from the mathematical
technology of symbols for efficiently handling the types of polylogarithm
functions which frequently appear in multi-loop computations. The symbol for
all two-loop MHV amplitudes in planar SYM theory is known, but explicit
analytic formulas for the amplitudes are hard to come by except in special
limits where things simplify, such as multi-Regge kinematics. By applying
symbology we obtain a formula for the leading behavior of the imaginary part
(the Mandelstam cut contribution) of this amplitude in multi-Regge kinematics
for any number of gluons. Our result predicts a simple recursive structure
which agrees with a direct BFKL computation carried out in a parallel
publication.Comment: 20 pages, 2 figures. v2: minor correction
A Grassmannian Etude in NMHV Minors
Arkani-Hamed, Cachazo, Cheung and Kaplan have proposed a Grassmannian
formulation for the S-matrix of N=4 Yang-Mills as an integral over link
variables. In parallel work, the connected prescription for computing tree
amplitudes in Witten's twistor string theory has also been written in terms of
link variables. In this paper we extend the six- and seven-point results of
arXiv:0909.0229 and arXiv:0909.0499 by providing a simple analytic proof of the
equivalence between the two formulas for all tree-level NMHV superamplitudes.
Also we note that a simple deformation of the connected prescription integrand
gives directly the ACCK Grassmannian integrand in the limit when the
deformation parameters equal zero.Comment: 17 page
Probing empirical contact networks by simulation of spreading dynamics
Disease, opinions, ideas, gossip, etc. all spread on social networks. How
these networks are connected (the network structure) influences the dynamics of
the spreading processes. By investigating these relationships one gains
understanding both of the spreading itself and the structure and function of
the contact network. In this chapter, we will summarize the recent literature
using simulation of spreading processes on top of empirical contact data. We
will mostly focus on disease simulations on temporal proximity networks --
networks recording who is close to whom, at what time -- but also cover other
types of networks and spreading processes. We analyze 29 empirical networks to
illustrate the methods
Twistors, Harmonics and Holomorphic Chern-Simons
We show that the off-shell N=3 action of N=4 super Yang-Mills can be written
as a holomorphic Chern-Simons action whose Dolbeault operator is constructed
from a complex-real (CR) structure of harmonic space. We also show that the
local space-time operators can be written as a Penrose transform on the coset
SU(3)/(U(1) \times U(1)). We observe a strong similarity to ambitwistor space
constructions.Comment: 34 pages, 3 figures, v2: replaced with published version, v3: Added
referenc
Unification of Residues and Grassmannian Dualities
The conjectured duality relating all-loop leading singularities of n-particle
N^(k-2)MHV scattering amplitudes in N=4 SYM to a simple contour integral over
the Grassmannian G(k,n) makes all the symmetries of the theory manifest. Every
residue is individually Yangian invariant, but does not have a local space-time
interpretation--only a special sum over residues gives physical amplitudes. In
this paper we show that the sum over residues giving tree amplitudes can be
unified into a single algebraic variety, which we explicitly construct for all
NMHV and N^2MHV amplitudes. Remarkably, this allows the contour integral to
have a "particle interpretation" in the Grassmannian, where higher-point
amplitudes can be constructed from lower-point ones by adding one particle at a
time, with soft limits manifest. We move on to show that the connected
prescription for tree amplitudes in Witten's twistor string theory also admits
a Grassmannian particle interpretation, where the integral over the
Grassmannian localizes over the Veronese map from G(2,n) to G(k,n). These
apparently very different theories are related by a natural deformation with a
parameter t that smoothly interpolates between them. For NMHV amplitudes, we
use a simple residue theorem to prove t-independence of the result, thus
establishing a novel kind of duality between these theories.Comment: 56 pages, 11 figures; v2: typos corrected, minor improvement
Integrable spin chains and scattering amplitudes
In this review we show that the multi-particle scattering amplitudes in N=4
SYM at large Nc and in the multi-Regge kinematics for some physical regions
have the high energy behavior appearing from the contribution of the Mandelstam
cuts in the complex angular momentum plane of the corresponding t-channel
partial waves. These Mandelstam cuts or Regge cuts are resulting from gluon
composite states in the adjoint representation of the gauge group SU(Nc). In
the leading logarithmic approximation (LLA) their contribution to the six point
amplitude is in full agreement with the known two-loop result.
The Hamiltonian for the Mandelstam states constructed from n gluons in LLA
coincides with the local Hamiltonian of an integrable open spin chain. We
construct the corresponding wave functions using the integrals of motion and
the Baxter-Sklyanin approach.Comment: Invited review for a special issue of Journal of Physics A devoted to
"Scattering Amplitudes in Gauge Theories", R. Roiban(ed), M. Spradlin(ed), A.
Volovich (ed
Generic multiloop methods and application to N=4 super-Yang-Mills
We review some recent additions to the tool-chest of techniques for finding
compact integrand representations of multiloop gauge-theory amplitudes -
including non-planar contributions - applicable for N=4 super-Yang-Mills in
four and higher dimensions, as well as for theories with less supersymmetry. We
discuss a general organization of amplitudes in terms of purely cubic graphs,
review the method of maximal cuts, as well as some special D-dimensional
recursive cuts, and conclude by describing the efficient organization of
amplitudes resulting from the conjectured duality between color and kinematic
structures on constituent graphs.Comment: 42 pages, 18 figures, invited review for a special issue of Journal
of Physics A devoted to "Scattering Amplitudes in Gauge Theories", v2 minor
corrections, v3 added reference
The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
We give a representation of the parity-even part of the planar two-loop
six-gluon MHV amplitude of N=4 super-Yang-Mills theory, in terms of
loop-momentum integrals with simple dual conformal properties. We evaluate the
integrals numerically in order to test directly the ABDK/BDS all-loop ansatz
for planar MHV amplitudes. We find that the ansatz requires an additive
remainder function, in accord with previous indications from strong-coupling
and Regge limits. The planar six-gluon amplitude can also be compared with the
hexagonal Wilson loop computed by Drummond, Henn, Korchemsky and Sokatchev in
arXiv:0803.1466 [hep-th]. After accounting for differing singularities and
other constants independent of the kinematics, we find that the Wilson loop and
MHV-amplitude remainders are identical, to within our numerical precision. This
result provides non-trivial confirmation of a proposed n-point equivalence
between Wilson loops and planar MHV amplitudes, and suggests that an additional
mechanism besides dual conformal symmetry fixes their form at six points and
beyond.Comment: 49 pages, RevTex, 2 figure file, v2 minor correction
Hidden Simplicity of Gauge Theory Amplitudes
These notes were given as lectures at the CERN Winter School on Supergravity,
Strings and Gauge Theory 2010. We describe the structure of scattering
amplitudes in gauge theories, focussing on the maximally supersymmetric theory
to highlight the hidden symmetries which appear. Using the BCFW recursion
relations we solve for the tree-level S-matrix in N=4 super Yang-Mills theory,
and describe how it produces a sum of invariants of a large symmetry algebra.
We review amplitudes in the planar theory beyond tree-level, describing the
connection between amplitudes and Wilson loops, and discuss the implications of
the hidden symmetries.Comment: 46 pages, 15 figures. v2 ref added, typos fixe
Situational Awareness of Influenza Activity Based on Multiple Streams of Surveillance Data Using Multivariate Dynamic Linear Model
BACKGROUND: Multiple sources of influenza surveillance data are becoming more available; however integration of these data streams for situational awareness of influenza activity is less explored. METHODS AND RESULTS: We applied multivariate time-series methods to sentinel outpatient and school absenteeism surveillance data in Hong Kong during 2004-2009. School absenteeism data and outpatient surveillance data experienced interruptions due to school holidays and changes in public health guidelines during the pandemic, including school closures and the establishment of special designated flu clinics, which in turn provided 'drop-in' fever counts surveillance data. A multivariate dynamic linear model was used to monitor influenza activity throughout epidemics based on all available data. The inferred level followed influenza activity closely at different times, while the inferred trend was less competent with low influenza activity. Correlations between inferred level and trend from the multivariate model and reference influenza activity, measured by the product of weekly laboratory influenza detection rates and weekly general practitioner influenza-like illness consultation rates, were calculated and compared with those from univariate models. Over the whole study period, there was a significantly higher correlation (rho = 0.82, p</=0.02) for the inferred trend based on the multivariate model compared to other univariate models, while the inferred trend from the multivariate model performed as well as the best univariate model in the pre-pandemic and the pandemic period. The inferred trend and level from the multivariate model was able to match, if not outperform, the best univariate model albeit with missing data plus drop-in and drop-out of different surveillance data streams. An overall influenza index combining level and trend was constructed to demonstrate another potential use of the method. CONCLUSIONS: Our results demonstrate the potential use of multiple streams of influenza surveillance data to promote situational awareness about the level and trend of seasonal and pandemic influenza activity.published_or_final_versio
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