On-Shell Methods in Perturbative QCD

We review on-shell methods for computing multi-parton scattering amplitudes in perturbative QCD, utilizing their unitarity and factorization properties. We focus on aspects which are useful for the construction of one-loop amplitudes needed for phenomenological studies at the Large Hadron Collider.Comment: 49 pages, 15 figures. v2: minor typos correcte

The Forces Applied by Cilia Depend Linearly on Their Frequency Due to Constant Geometry of the Effective Stroke

AbstractMucus propelling cilia are excitable by many stimulants, and have been shown to increase their beating frequency up to threefold, by physiological extracellular stimulants, such as adenosine-triphosphate, acetylcholine, and others. This is thought to represent the evolutionary adaptation of mucociliary systems to the need of rapid and efficient cleansing the airways of foreign particles. However, the mucus transport velocity depends not only on the beat frequency of the cilia, but on their beat pattern as well, especially in the case of mucus bearing cilia that beat in a complex, three-dimensional fashion. In this study, we directly measured the force applied by live ciliary tissues with an atomic force microscope, and found that it increases linearly with the beating frequency. This implies that the arc swept by the cilia during their effective stroke remains unchanged during frequency increase, thus leading to a linear dependence of transport velocity on the beat frequency. Combining the atomic force microscope measurements with optical measurements, we have indications that the recovery stroke is performed on a less inclined plane, leading to an effective shortening of the overall path traveled by the cilia tip during this nontransporting phase of their beat pattern. This effect is observed to be independent of the type of stimulant (temperature or chemical), chemical (adenosine-triphosphate or acetylcholine), or concentration (1μM–100μM), indicating that this behavior may result from internal details of the cilium mechanical structure

Algebraic Systems Biology: A Case Study for the Wnt Pathway

Steady state analysis of dynamical systems for biological networks give rise to algebraic varieties in high-dimensional spaces whose study is of interest in their own right. We demonstrate this for the shuttle model of the Wnt signaling pathway. Here the variety is described by a polynomial system in 19 unknowns and 36 parameters. Current methods from computational algebraic geometry and combinatorics are applied to analyze this model.Comment: 24 pages, 2 figure

Advanced Techniques for Multiparton Loop Calculations: A Minireview

We present an overview of techniques developed in recent years for the efficient calculation of one-loop multiparton amplitudes, in particular those relying on unitarity and collinear factorization.Comment: 5 pages, LaTeX/aipproc, presented at DIS '97, Chicago, IL, April 14-18, 199

Patents and R&D: Searching for a Lag Structure

This paper extends earlier work on the R&D to patents relationship (Pakes-Griliches 1980, and Hausman, Hall, and Griliches, 1984) to a larger but shorter panel of firms. Using both non-linear least squares and Poisson type models to treat the problem of discreteness in the dependent variable the paper tries to discern the lag structure of this relationship in greater detail. Since the available time series are short, two different approaches are pursued in trying to solve the lag truncation problem: In the first the influence of the unseen past is assumed to decline geometrically; in the second,the unobserved past series are assumed to have followed a low order autoregression. Neither approach yields strong evidence of a long lag. The available sample, though numerically large,turns out not to be particularly informative on this question. It does reconfirm, however, a significant effect of R&D on patenting (with most of it occurring in the first year or two) and the presence of rather wide and semi-permanent differences among firms in their patenting policies.

Patents and R&D: Is There A Lag?

This paper extends earlier work on the RID to patents relationship (Pakes-Griliches 1980, and Hausman, Hall, and Griliches,1984) to a larger but shorter panel of firms. The focus of the paper is on solving a number of econometric problems associated with the discreteness of the dependent variable and the shortness of the panel in the time dimension. We compare weighted nonlinear least squares as wellas Poisson-type models as solutions to the former problem. In attempting to estimate a lag structure on R&D in the absence of a sufficient history of the variable, we take two approaches: first, we use the conditional version of the negative binomial model, and second, we estimate the R&D variable itself as a low order stochastic process and use this information to control for unobserved R&D. R&D itself turns out to befairly well approximated by a random walk. Neither approach yields strong evidence of a long lag. The available sample, though numerically large, turns out not to be particularily informative on this question. It does reconfirm, however, a significant effect of R&D on patenting (with most of it occuring in the first year) and the presence of rather wide and semi-permanent differences among firms in their patenting policies.

The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory

We present an expression for the leading-color (planar) four-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2 e dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around e=0, and obtain analytic expressions for the poles from 1/e^8 through 1/e^4. We give numerical results for the coefficients of the 1/e^3 and 1/e^2 poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/e^2 coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing zeta_3^2, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimate the two constants in the strong-coupling expansion of the cusp anomalous dimension that are known from string theory. The estimate works to 2.6% and 5% accuracy, providing non-trivial evidence in support of the AdS/CFT correspondence. We also use the known constants in the strong-coupling expansion as additional input to provide approximations to the cusp anomalous dimension which should be accurate to under one percent for all values of the coupling. When the evaluations of the integrals are completed through the finite terms, it will be possible to test the iterative, exponentiated structure of the finite terms in the four-loop four-point amplitude, which was uncovered earlier at two and three loops.Comment: 72 pages, 15 figures, v2 minor correction