Abstract We study Hessian estimators for functions defined over an $n$-dimensional complete analytic Riemannian manifold. introduce new stochastic zeroth-order using $O (1)$ function evaluations. show that, real-valued $f$, our estimator achieves a bias bound of order $ O ( \gamma \delta ^2 ) $, where depends on both the Levi–Civita connection and $\delta is finite difference step size. To best...

Basic theoretical treatments of quantum beats are presented using the effective Hamiltonian method and the density matrix method. To describe the states involved in quantum beats, the molecular-eigen state basis set and the zeroth order basis set are introduced. Based on these basis sets for the two-state model, the condition under which molecular coherence can be created is discussed.

"The aim of this paper is to develop a probability model describing the variation in...total out-migration [using] micro-level data. The parameters involved in the models are estimated with the help of [the] method of moment, proportion of zeroth cell and one'th cell respectively, [and] the suitability of [the] model [is] tested through observed demographic survey data [for India]."

Nonadditive composition rules for several physical quantities are treated in thermodynamics. It is argued that the zeroth law defines the existence of their additive forms, the formal logarithms. A further principle, the universal thermostat independence leads to a particular formal logarithm, equivalent to Tsallis entropy Sq. We connect q with generalized susceptibilities of the thermostat.

In this work we address the problem of convex optimization in a multi-agent setting where objective is to minimize mean local cost functions whose derivatives are not available (e.g. black-box models). Moreover agents can only communicate with neighbors according connected network topology. Zeroth-order (ZO) has recently gained increasing attention federated learning and scenarios exploiting fi...