Introduction Conclusions References Tables Figures

This paper contains a survey of the spectral theory of periodically correlated and almost periodically correlated stochastic processes. These processes are also called cyclostationary and almost cyclostationary, and we give give some remarks concerning the historical development of the two nomenclatures. In this paper we survey the spectral theory of the covariance, the estimation of the Fourie...

there are many different ways to subdivide the spectrum of a bounded linear operator; some of them aremotivated by applications to physics (in particular, quantum mechanics). in this study, the relationship betweenthe subdivisions of spectrum which are not required to be disjoint and goldberg's classification are given.moreover, these subdivisions for some summability methods are studied.

We consider analysis of sparsely sampled multilevel functional data, where the basic observational unit is a function and data have a natural hierarchy of basic units. An example is when functions are recorded at multiple visits for each subject. Multilevel functional principal component analysis (MFPCA; Di et al. 2009) was proposed for such data when functions are densely recorded. Here we con...

In multisensor target tracking, each sensor can have its own target state estimate based on the local sensor measurements. Most existing communication networks between local trackers/sensors transmit to a fusion center the local track estimates–sometimes without any estimation error covariances, sometimes with partial covariance information and only rarely with full covariance information. In o...

A perturbative renormalization group is formulated for the study of Hamiltonian light-front field theory near a critical Gaussian fixed point. The only light-front renormalization group transformations found here that can be approximated by dropping irrelevant operators and using perturbation theory near Gaussian fixed volumes, employ invariant-mass cutoffs. These cutoffs violate covariance and...

Abstract In data assimilation (DA), the estimation of background error covariance operator is a classical and still open topic. However, this often modeled using empirical information. order to exploit at best potential knowledge physics, present study proposes method derive operators from underlying equations. addition, Green’s kernels can be used model are naturally linked them. Therefore, eq...

Recursive credibility estimation is discussed from the viewpoint of linear filtering theory. A conjunction of geometric mterpretation and the innovation approach leads to general algorithms not developed before. Moreover, covariance characterizations considered by other researchers drop our elegantly as a result of geometric considerations. Examples are presented of Kalman type filters valid fo...

Abstract Obtaining the expectation value of an observable on a quantum computer is crucial step in variational algorithms. For complicated observables such as molecular electronic Hamiltonians, one strategies to present linear combination measurable fragments. The main problem this approach large number measurements required for accurate estimation observable’s value. We consider three previous...