We establish improved mean value estimates associated with the number of integer solutions certain systems diagonal equations, in some instances attaining sharpest conjectured conclusions. This is first occasion on which bounds this quali

For pattern recognition problems where a small set of relevant objects should be retrieved from a (very) large set of irrelevant objects, standard evaluation criteria are often insufficient. For these situations often the precision-recall curve is used. An often-employed scalar measure derived from this curve is the mean precision, that estimates the average precision over all values of the rec...

We introduce the concept of mean-field optimal control which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of interacting agents. While in the class...

We consider parameter estimation for time-dependent locally stationary long-memory processes. The asymptotic distribution of an estimator based on the local infinite autoregressive representation is derived, and asymptotic formulas for the mean squared error of the estimator, and the asymptotically optimal bandwidth are obtained. In spite of long memory, the optimal bandwidth turns out to be of...

A control strategy based on a mean-variance objective and expected value constraints is proposed for systems with additive and multiplicative stochastic uncertainty. Subject to a mean square stabilizability condition, the receding horizon objective can be obtained by solving a system of Lyapunov equations. An algorithm is proposed for computing the unconstrained optimal control law, which is th...