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...

A compact Zeroth Order Resonator Antenna (ZORA) is implemented as a part of course work for Radio Frequency Integrated Circuits and Systems (E8-242). This work is based on [1] . Due to the unique properties of Compact Right/Left Handed (CRLH) transmission lines, the size of the antenna is independent of the frequency of operation. This compact structure is made of two unit cells each comprising...

We propose a method for zeroth order stochastic convex optimization that attains the suboptimality rate of Õ(n7T−1/2) after T queries for a convex bounded function f : R → R. The method is based on a random walk (the Ball Walk) on the epigraph of the function. The randomized approach circumvents the problem of gradient estimation, and appears to be less sensitive to noisy function evaluations c...

We study the most general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the zeroth order operator Z in the semi-classical limit s → ∞. We use Witten’s method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. The paper contains...

We study the most general conditions under which the computations of the index of a perturbed Dirac operator Ds = D + sZ localize to the singular set of the zeroth order operator Z in the semi-classical limit s → ∞. We use Witten’s method to compute the index of D by doing a combinatorial computation involving local data at the nondegenerate singular points of the operator Z. The paper contains...

The nite-temperature renormalization group is formulated via the Wilson-Kadanoo blocking transformation. Momentum modes and the Matsubara frequencies are coupled by constraints from a smearing function which plays the role of an infrared cutoo regulator. Using the scalar 4 theory as an example, we consider four general types of smearing functions and show that, to zeroth-order in the derivative...

A broadband zeroth-order resonant (ZOR) antenna based on asymmetric coplanar waveguide (ACPW) is presented. By adopting the epsilon negative transmission line (ENG-TL), a zeroth-order resonance mode can be achieved. We employ an asymmetric coplanar waveguide structure which offers the design freedom to realize the broadband ZOR antenna, where the antenna’s bandwidth is characterized by the equi...