All Two-Loop Feynman Integrals for Five-Point One-Mass Scattering.

We compute the complete set of two-loop master integrals for the scattering of four massless particles and a massive one. Our results are ready for phenomenological applications, removing a major obstacle to the computation of complete next-to-next-to-leading order QCD corrections to processes such as the production of a H/Z/W boson in association with two jets at the LHC. Furthermore, they open the door to new investigations into the structure of quantum-field theories and provide precious analytic data for studying the mathematical properties of Feynman integrals.

Cluster Algebras for Feynman Integrals.

We initiate the study of cluster algebras in Feynman integrals in dimensional regularization. We provide evidence that four-point Feynman integrals with one off-shell leg are described by a C_{2} cluster algebra, and we find cluster adjacency relations that restrict the allowed function space. By embedding C_{2} inside the A_{3} cluster algebra, we identify these adjacencies with the extended Steinmann relations for six-particle massless scattering.

All Master Integrals for Three-Jet Production at Next-to-Next-to-Leading Order.

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by identifying integrals with constant leading singularities, in D space-time dimensions. These integrals evaluate to Q-linear combinations of multiple polylogarithms of uniform weight at each order in the expansion in the dimensional regularization parameter and are in agreement with previous conjectures for nonplanar pentagon functions.

Analytic Form of the Full Two-Loop Five-Gluon All-Plus Helicity Amplitude.

We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude and extract the finite hard function.

Analytic Result for a Two-Loop Five-Particle Amplitude.

We compute the symbol of the full-color two-loop five-particle amplitude in N=4 super Yang-Mills theory, including all nonplanar subleading-color terms. The amplitude is written in terms of permutations of Parke-Taylor tree-level amplitudes and pure functions to all orders in the dimensional regularization parameter, in agreement with previous conjectures. The answer has the correct collinear limits and infrared factorization properties, allowing us to define a finite remainder function.

Scattering Amplitudes from Superconformal Ward Identities.

We consider finite superamplitudes of N=1 matter, and use superconformal symmetry to derive powerful first-order differential equations for them. Because of on-shell collinear singularities, the Ward identities have an anomaly, which is obtained from lower-loop information. We show that in the five-particle case, the solution to the equations is uniquely fixed by the expected analytic behavior.

[Multifunctional computer system for psychophysiologic selection for "human-technology" occupations].

Psychophysiologic selection for "human-technics" occupations. Expert evaluations determine composition and value of occupational traits for each occupation, fitness is assessed through match between the candidate's test parameters and psychophysiologic standard for each occupation.