Analytic Results for Massless Three-Loop Form Factors

We evaluate, exactly in d, the master integrals contributing to massless three-loop QCD form factors. The calculation is based on a combination of a method recently suggested by one of the authors (R.L.) with other techniques: sector decomposition implemented in FIESTA, the method of Mellin--Barnes representation, and the PSLQ algorithm. Using our results for the master integrals we obtain analytical expressions for two missing constants in the ep-expansion of the two most complicated master integrals and present the form factors in a completely analytic form.Comment: minor revisions, to appear in JHE

Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

A Simple Iterative Model Accurately Captures Complex Trapline Formation by Bumblebees Across Spatial Scales and Flower Arrangements

PMCID: PMC3591286This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited

Force Generation upon T Cell Receptor Engagement

T cells are major players of adaptive immune response in mammals. Recognition of an antigenic peptide in association with the major histocompatibility complex at the surface of an antigen presenting cell (APC) is a specific and sensitive process whose mechanism is not fully understood. The potential contribution of mechanical forces in the T cell activation process is increasingly debated, although these forces are scarcely defined and hold only limited experimental evidence. In this work, we have implemented a biomembrane force probe (BFP) setup and a model APC to explore the nature and the characteristics of the mechanical forces potentially generated upon engagement of the T cell receptor (TCR) and/or lymphocyte function-associated antigen-1 (LFA-1). We show that upon contact with a model APC coated with antibodies towards TCR-CD3, after a short latency, the T cell developed a timed sequence of pushing and pulling forces against its target. These processes were defined by their initial constant growth velocity and loading rate (force increase per unit of time). LFA-1 engagement together with TCR-CD3 reduced the growing speed during the pushing phase without triggering the same mechanical behavior when engaged alone. Intracellular Ca2+ concentration ([Ca2+]i) was monitored simultaneously to verify the cell commitment in the activation process. [Ca2+]i increased a few tens of seconds after the beginning of the pushing phase although no strong correlation appeared between the two events. The pushing phase was driven by actin polymerization. Tuning the BFP mechanical properties, we could show that the loading rate during the pulling phase increased with the target stiffness. This indicated that a mechanosensing mechanism is implemented in the early steps of the activation process. We provide here the first quantified description of force generation sequence upon local bidimensional engagement of TCR-CD3 and discuss its potential role in a T cell mechanically-regulated activation process

On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes

We propose a first implementation of the integrand-reduction method for two-loop scattering amplitudes. We show that the residues of the amplitudes on multi-particle cuts are polynomials in the irreducible scalar products involving the loop momenta, and that the reduction of the amplitudes in terms of master integrals can be realized through polynomial fitting of the integrand, without any apriori knowledge of the integral basis. We discuss how the polynomial shapes of the residues determine the basis of master integrals appearing in the final result. We present a four-dimensional constructive algorithm that we apply to planar and non-planar contributions to the 4- and 5-point MHV amplitudes in N=4 SYM. The technique hereby discussed extends the well-established analogous method holding for one-loop amplitudes, and can be considered a preliminary study towards the systematic reduction at the integrand-level of two-loop amplitudes in any gauge theory, suitable for their automated semianalytic evaluation.Comment: 26 pages, 11 figure

The bashful and the boastful : prestigious leaders and social change in Mesolithic Societies

The creation and maintenance of influential leaders and authorities is one of the key themes of archaeological and historical enquiry. However the social dynamics of authorities and leaders in the Mesolithic remains a largely unexplored area of study. The role and influence of authorities can be remarkably different in different situations yet they exist in all societies and in almost all social contexts from playgrounds to parliaments. Here we explore the literature on the dynamics of authority creation, maintenance and contestation in egalitarian societies, and discuss the implications for our interpretation and understanding of the formation of authorities and leaders and changing social relationships within the Mesolithic

Two-Loop Soft Corrections and Resummation of the Thrust Distribution in the Dijet Region

The thrust distribution in electron-positron annihilation is a classical precision QCD observable. Using renormalization group (RG) evolution in Laplace space, we perform the resummation of logarithmically enhanced corrections in the dijet limit, $T\to 1$ to next-to-next-to-leading logarithmic (NNLL) accuracy. We independently derive the two-loop soft function for the thrust distribution and extract an analytical expression for the NNLL resummation coefficient $g_3$. To combine the resummed expressions with the fixed-order results, we derive the $\log(R)$-matching and $R$-matching of the NNLL approximation to the fixed-order NNLO distribution.Comment: 50 pages, 12 figures, 1 table. Few minor changes. Version accepted for publication in JHE