A New Approach to Robot’s Imitation of Behaviors by Decomposition of Multiple-Valued Relations

Relation decomposition has been used for FPGA mapping, layout optimization, and data mining. Decision trees are very popular in data mining and robotics. We present relation decomposition as a new general-purpose machine learning method which generalizes the methods of inducing decision trees, decision diagrams and other structures. Relation decomposition can be used in robotics also in place of classical learning methods such as Reinforcement Learning or Artificial Neural Networks. This paper presents an approach to imitation learning based on decomposition. A Head/Hand robot learns simple behaviors using features extracted from computer vision, speech recognition and sensors

Single-valued periods and multiple zeta values

The values at 1 of single-valued multiple polylogarithms span a certain subalgebra of multiple zeta values. In this paper, the properties of this algebra are studied from the point of view of motivic periods

Heterotic-string amplitudes at one loop: modular graph forms and relations to open strings

We investigate one-loop four-point scattering of non-abelian gauge bosons in heterotic string theory and identify new connections with the corresponding open-string amplitude. In the low-energy expansion of the heterotic-string amplitude, the integrals over torus punctures are systematically evaluated in terms of modular graph forms, certain non-holomorphic modular forms. For a specific torus integral, the modular graph forms in the low-energy expansion are related to the elliptic multiple zeta values from the analogous open-string integrations over cylinder boundaries. The detailed correspondence between these modular graph forms and elliptic multiple zeta values supports a recent proposal for an elliptic generalization of the single-valued map at genus zero.Comment: 57+22 pages, v2: references updated, version published in JHE

Quantum Analogs of Tensor Product Representations of su(1,1)

We study representations of $U_q(su(1,1))$ that can be considered as quantum analogs of tensor products of irreducible *-representations of the Lie algebra $su(1,1)$. We determine the decomposition of these representations into irreducible *-representations of $U_q(su(1,1))$ by diagonalizing the action of the Casimir operator on suitable subspaces of the representation spaces. This leads to an interpretation of the big $q$-Jacobi polynomials and big $q$-Jacobi functions as quantum analogs of Clebsch-Gordan coefficients