23,890 research outputs found
A class of relations among multiple zeta values
We prove a new class of relations among multiple zeta values (MZV's) which
contains Ohno's relation. We also give the formula for the maximal number of
independent MZV's of fixed weight, under our new relations. To derive our
formula for MZV's we consider the Newton series whose values at non-negative
integers are finite multiple harmonic sums.Comment: 36 pages, presentation improved, to appear in Journal of Number
Theor
Optimization Algorithms Based on Renormalization Group
Global changes of states are of crucial importance in optimization
algorithms. We review some heuristic algorithms in which global updates are
realized by a sort of real-space renormalization group transformation. Emphasis
is on the relationship between the structure of low-energy excitations and
``block-spins'' appearing in the algorithms. We also discuss the implication of
existence of a finite-temperature phase transition on the computational
complexity of the ground-state problem.Comment: 7 pages, 2 figure
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