We extend the block filtration, defined by Brown based on work of Charlton, to all motivic multiple zeta values, and study relations compatible with this filtration. construct a Lie algebra describing among values modulo terms lower degree, proving Charlton's cyclic insertion conjecture in structure, showing existence ‘block shuffle’ relation, dihedral symmetry, differential relation.

Abstract. The sum formula is a basic identity of multiple zeta values that expresses a Riemann zeta value as a homogeneous sum of multiple zeta values of a given dimension. This formula was already known to Euler in the dimension two case, conjectured in the early 1990s for higher dimensions and then proved by Granville and Zagier independently. Recently a weighted form of Euler’s formula was o...

This paper introduces one approach f o r the combination of classifiers, in a context that each classifier can ofler not only class labels but also Ihe corresponding measurement values. This approach is called the Linear Confidence Accumvlation method (LCA). The three steps that LCA consists of are: first, measurement values are transformed into confidence values; second, a confidence aggregati...

Using the combinatorial description of shuffle product, we prove or reformulate several shuffle product formulas of multiple zeta values, including a general formula of the shuffle product of two multiple zeta values, some restricted shuffle product formulas of the product of two multiple zeta values, and a restricted shuffle product formula of the product of n multiple zeta values.