• Let Ak denote the set of methods that observe a sequence of data pairs Y t = (F (θ, X ), F (τ , X )), 1 ≤ t ≤ k, and return an estimate θ̂(k) ∈ Θ. • Let FG denote the class of functions we want to optimize, where for each (F, P ) ∈ FG the subgradient g(θ;X) satisfies EP [‖g(θ;X)‖2∗] ≤ G. • For each A ∈ Ak and (F, P ) ∈ FG, consider the optimization gap: k(A, F, P,Θ) := f (θ̂(k))− inf θ∈Θ f (θ) ...

The minimization of convex functions which are only available through partial and noisy information is a key methodological problem in many disciplines. In this paper we consider convex optimization with noisy zero-th order information, that is noisy function evaluations at any desired point. We focus on problems with high degrees of smoothness, such as logistic regression. We show that as oppo...

The spectral and scattering theory is investigated for a generalization, to scattering metrics on two-dimensional compact manifolds with boundary, of the class of smooth potentials on R which are homogeneous of degree zero near infinity. The most complete results require the additional assumption that the restriction of the potential to the circle(s) at infinity be Morse. Generalized eigenfunct...

Translating a graded morphogen distribution into tight response borders is central to all developmental processes. Yet, the molecular mechanisms generating such behavior are poorly understood. During patterning of the Drosophila embryonic ventral ectoderm, a graded mitogen-activated protein kinase (MAPK) activation is converted into an all-or-none degradation switch of the Yan transcriptional r...

The general structure of the 1/m corrections at zero recoil is studied. The relevant matrix elements are forward matrix elements of local higher dimensional operators and their time ordered products with higher order terms from the Lagrangian. These matrix elements may be classified in a simple way and the analysis at the non recoil point for the form factor of heavy quark currents simplifies d...

Previous studies of the stability of the second-order backward differentiation formula have concluded that stability is possible only if restrictions are placed on the stepsize ratios, for example, limiting the ratio to some value less than 1 + fi. However, actual implementations of the BDFs differ from the usual theoretical models of such methods; in particular, practical codes use scaled deri...

The electromagnetic response of a zero-order metal grating having a primary deep short-period component and a shallow long-period component is modeled. It is found that such a metal grating has an unusual surface-plasmon-polariton band structure and exhibits strong selective absorption of incident radiation. This opens up potential for designing metal surfaces with specific optical response fea...

A novel zero-order resonator has been designed by an optical surface transformation (OST) method. The resonator proposed here has many novel features. Firstly, the mode volume can be very small (e.g. in the subwavelength scale). Secondly, the resonator is open (no reflecting walls are utilized) and resonant effects can be found in a continuous spectrum (i.e. a continuum of eigenmodes). Thirdly,...

In system identi cation, estimates of the unknown system model orders are often required. An algorithm for estimating model orders is described which looks at input/output data covariance matrix eigenvectors. When model orders are overestimated, zeros appear in the noise subspace eigenvectors. The number of zeros present can be used to estimate model orders.

This study investigated the potential effects of egg quality indices at 95% confidence level in order to minimize quality loss during different storage conditions. The chicken and quail eggs’ quality indices including weight, albumen index, yolk index, Haugh index in fresh eggs as well as after storing in moist sawdust, oil, and refrigerator were measured for six weeks. The results revealed tha...