325 research outputs found
On the Factorisation of the Connected Prescription for Yang-Mills Amplitudes
We examine factorisation in the connected prescription of Yang-Mills
amplitudes. The multi-particle pole is interpreted as coming from representing
delta functions as meromorphic functions. However, a naive evaluation does not
give a correct result. We give a simple prescription for the integration
contour which does give the correct result. We verify this prescription for a
family of gauge-fixing conditions.Comment: 16 pages, 1 figur
Traintrack Calabi-Yaus from Twistor Geometry
We describe the geometry of the leading singularity locus of the traintrack
integral family directly in momentum twistor space. For the two-loop case,
known as the elliptic double box, the leading singularity locus is a genus one
curve, which we obtain as an intersection of two quadrics in .
At three loops, we obtain a K3 surface which arises as a branched surface over
two genus-one curves in . We present an
analysis of its properties. We also discuss the geometry at higher loops and
the supersymmetrization of the construction.Comment: 23 pages, 5 figure
Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient
We consider a multidimensional diffusion X with drift coefficient
b({\alpha},X(t)) and diffusion coefficient {\epsilon}{\sigma}({\beta},X(t)).
The diffusion is discretely observed at times t_k=k{\Delta} for k=1..n on a
fixed interval [0,T]. We study minimum contrast estimators derived from the
Gaussian process approximating X for small {\epsilon}. We obtain consistent and
asymptotically normal estimators of {\alpha} for fixed {\Delta} and
{\epsilon}\rightarrow0 and of ({\alpha},{\beta}) for {\Delta}\rightarrow0 and
{\epsilon}\rightarrow0. We compare the estimators obtained with various methods
and for various magnitudes of {\Delta} and {\epsilon} based on simulation
studies. Finally, we investigate the interest of using such methods in an
epidemiological framework.Comment: 31 pages, 2 figures, 2 table
Defect multiplets of N=1 supersymmetry in 4d
Any 4d theory possessing supersymmetry admits a so called
-multiplet, containing the conserved energy-momentum tensor and
supercurrent. When a defect is introduced into such a theory, the
-multiplet receives contributions localised on the defect, which
indicate the breaking of some translation symmetry and consequently also some
supersymmetries. We call this the defect multiplet. We classify such terms
corresponding to half-BPS defects which can be either three-dimensional,
preserving 3d , or two-dimensional, preserving
. The new terms localised on the defect furnish multiplets
of the reduced symmetry and give rise to the displacement operator
Approximation of epidemic models by diffusion processes and their statistical inference
Multidimensional continuous-time Markov jump processes on
form a usual set-up for modeling -like epidemics. However,
when facing incomplete epidemic data, inference based on is not easy
to be achieved. Here, we start building a new framework for the estimation of
key parameters of epidemic models based on statistics of diffusion processes
approximating . First, \previous results on the approximation of
density-dependent -like models by diffusion processes with small diffusion
coefficient , where is the population size, are
generalized to non-autonomous systems. Second, our previous inference results
on discretely observed diffusion processes with small diffusion coefficient are
extended to time-dependent diffusions. Consistent and asymptotically Gaussian
estimates are obtained for a fixed number of observations, which
corresponds to the epidemic context, and for . A
correction term, which yields better estimates non asymptotically, is also
included. Finally, performances and robustness of our estimators with respect
to various parameters such as (the basic reproduction number), ,
are investigated on simulations. Two models, and , corresponding to
single and recurrent outbreaks, respectively, are used to simulate data. The
findings indicate that our estimators have good asymptotic properties and
behave noticeably well for realistic numbers of observations and population
sizes. This study lays the foundations of a generic inference method currently
under extension to incompletely observed epidemic data. Indeed, contrary to the
majority of current inference techniques for partially observed processes,
which necessitates computer intensive simulations, our method being mostly an
analytical approach requires only the classical optimization steps.Comment: 30 pages, 10 figure
On the Geometry of Null Polygons in Full N=4 Superspace
We discuss various formulations of null polygons in full, non-chiral N=4
superspace in terms of spacetime, spinor and twistor variables. We also note
that null polygons are necessarily fat along fermionic directions, a curious
fact which is compensated by suitable equivalence relations in physical
theories on this superspace.Comment: 25 pages, v2: comment on correlation functions adde
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