In this paper, we consider the issue of dual functions for the Bernstein basis which satisfy boundary conditions. The Jacobi weight function with the usual inner product in the Hilbert space are used. Some examples of the transformation matrices are given. Some figures for the weighted dual functions of the Bernstein basis with respect to the Jacobi weight function satisfying boundary condition...

Variational data assimilation problems arising in meteorology and oceanography require the solution of a regularized nonlinear least-squares problem. Practical solution algorithms are based on the incremental (Truncated Gauss-Newton) approach, which involves the iterative solution of a sequence of linear least-squares (quadratic minimization) sub-problems. Each sub-problem can be solved using a...

A new structure learning approach for Bayesian networks (BNs) based on dual genetic algorithm (DGA) is proposed in this paper. An individual of the population is represented as a dual chromosome composed of two chromosomes. The first chromosome represents the ordering among the BN nodes and the second represents the conditional dependencies among the ordered BN nodes. It is rigorously shown tha...

This paper provides a new formulation of second order stochastic target problems introduced in [19] by modifying the reference probability so as to allow for different scales. This new ingredient enables us to prove a dual formulation of the target problem as the supremum of the solutions of standard backward stochastic differential equations. In particular, in the Markov case, the dual problem...

A power assignment is an assignment of transmission power to each of the wireless nodes of a wireless network, so that the induced graph satisfies some desired properties. The cost of a power assignment is the sum of the assigned powers. In this paper, we consider the dual power assignment problem, in which each wireless node is assigned a highor low-power level, so that the induced graph is st...

Data of four layers flocks (#31-34) from North Carolina Layer Performance and Management Test of the Department of Agriculture and Consumer Services were used in the meta-analysis to find if an increase in space allowance can affect egg production traits in white and brown layers. Effects of space allowance of 310 and 413 cm2/bird on layers performance were compared in this study. The increase ...

Electron cryotomography can be used to solve the three-dimensional structures of individual large macromolecules, assemblies, and even small intact cells to medium (approximately 4-8 nm) resolution in a near-native state, but restrictions in the range of accessible views are a major limitation. Here we report on the design, characterization, and demonstration of a new "flip-flop" rotation stage...