Robust Coin Flipping

Alice seeks an information-theoretically secure source of private random data. Unfortunately, she lacks a personal source and must use remote sources controlled by other parties. Alice wants to simulate a coin flip of specified bias $\alpha$, as a function of data she receives from $p$ sources; she seeks privacy from any coalition of $r$ of them. We show: If $p/2 \leq r < p$, the bias can be any rational number and nothing else; if $0 < r < p/2$, the bias can be any algebraic number and nothing else. The proof uses projective varieties, convex geometry, and the probabilistic method. Our results improve on those laid out by Yao, who asserts one direction of the $r=1$ case in his seminal paper [Yao82]. We also provide an application to secure multiparty computation.Comment: 22 pages, 1 figur

Nutrient limitation can explain a rapid transition to synchrony in an upwelling-driven diatom community

Identifying the mechanisms controlling the temporal dynamics of ecological communities is key to understand their vulnerability to natural and anthropogenic impacts and to identify early warnings of critical transitions. At community level, inter-specific synchrony is an important indicator of ecosystem stability and variation in function. Using wavelet analysis on time-series of abundance of 12 dominant diatom species, sampled monthly (1994-2009) in a coastal upwelling embayment at the northern limit of the Canary Current Upwelling System, we find a sudden onset of synchrony between 1998 and 2002, concomitant with an increase in the amplitude of the upwelling index at different temporal scales. To better understand the underlying mechanism that could generate this sudden onset of synchrony among competitors, we analyzed a general model of competition between two species for two essential nutrients (e.g., nitrogen and silicate). We incorporate environmental variation by varying the concentration of one of the essential nutrients entering the system. Increase in the amplitude of environmental variation always leads to greater synchrony among competitors. This occurs because the system shifts from a state in which species are limited by different nutrients to one where species are often limited by the same nutrient. We show that the transition from asynchronous to synchronous dynamics can occur suddenly as the amplitude of environmental variation increases. While it is not possible to rule out alternative mechanisms, our model demonstrates that sudden changes in the extent of synchronization should be a common feature when species compete for essential nutrients in variable environments.En prensa3,38

Two-Loop Helicity Amplitudes for Quark-Gluon Scattering in QCD and Gluino-Gluon Scattering in Supersymmetric Yang-Mills Theory

We present the two-loop QCD helicity amplitudes for quark-gluon scattering, and for quark-antiquark annihilation into two gluons. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization. The transition rules for converting the amplitudes between the different variants are much more intricate than for the previously discussed case of gluon-gluon scattering. Summing our two-loop expressions over helicities and colors, and converting to conventional dimensional regularization, gives results in complete agreement with those of Anastasiou, Glover, Oleari and Tejeda-Yeomans. We describe the amplitudes for 2 to 2 scattering in pure N=1 supersymmetric Yang-Mills theory, obtained from the QCD amplitudes by modifying the color representation and multiplicities, and verify supersymmetry Ward identities in the FDH scheme.Comment: 77 pages. v2: corrected errors in eqs. (3.7) and (3.8) for one-loop assembly; remaining results unaffecte

Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory

We present the two-loop QCD helicity amplitudes for quark-quark and quark-antiquark scattering. These amplitudes are relevant for next-to-next-to-leading order corrections to (polarized) jet production at hadron colliders. We give the results in the `t Hooft-Veltman and four-dimensional helicity (FDH) variants of dimensional regularization and present the scheme dependence of the results. We verify that the finite remainder, after subtracting the divergences using Catani's formula, are in agreement with previous results. We also provide the amplitudes for gluino-gluino scattering in pure N=1 supersymmetric Yang-Mills theory. We describe ambiguities in continuing the Dirac algebra to D dimensions, including ones which violate fermion helicity conservation. The finite remainders after subtracting the divergences using Catani's formula, which enter into physical quantities, are free of these ambiguities. We show that in the FDH scheme, for gluino-gluino scattering, the finite remainders satisfy the expected supersymmetry Ward identities.Comment: arXiv admin note: substantial text overlap with arXiv:hep-ph/030416

An EBSD study of the deformation of service-aged 316 austenitic steel

Electron backscatter diffraction (EBSD) has been used to examine the plastic deformation of an ex-service 316 austenitic stainless steel at 297K and 823K (24 °C and 550 °C)at strain rates 3.5x10-3 to 4 x 10-7 s-1. The distribution of local misorientations was found to depend on the imposed plastic strain following a lognormal distribution at true strains 0.1. At 823 K (550 °C), the distribution of misorientations depended on the applied strain rate. The evolution of lattice misorientations with increasing plastic strain up to 0.23 was quantified using the metrics kernel average misorientation, average intragrain misorientation, and low angle misorientation fraction. For strain rate down to 10-5 s-1 all metrics were insensitive to deformation temperature, mode (tension vs. compression) and orientation of the measurement plane. The strain sensitivity of the different metrics was found to depend on the misorientation ranges considered in their calculation. A simple new metric, proportion of undeformed grains, is proposed for assessing strain in both aged and unaged material. Lattice misorientations build up with strain faster in aged steel than in un-aged material and most of the metrics were sensitive to the effects of thermal aging. Ignoring aging effects leads to significant overestimation of the strains around welds. The EBSD results were compared with nanohardness measurements and good agreement established between the two techniques of assessing plastic strain in aged 316 steel