A Chebyshev-based representation of the state vector is proposed for designing optimal control trajectories of unconstrained, linear, dynamic systems with quadratic performance indices. By approximating each state variable by a finite-term, shifted Chebyshev series, the linear quadratic (LQ) optimal control problem can be cast as a quadratic programming (QP) problem. In solving this QP problem,...

This paper presents a framework for solving the pure-state preparation problem using numerical optimal control. As an example, we consider case where number of qubits are dispersively coupled to readout cavity. We model open system quantum dynamics Markovian Lindblad master equation driven by external control pulses. The main result this develops basis density matrices (a parameterization) each...

This paper studies issues relating to the parameterization of probability distributions over binary data sets. Several such parameterizations of models for binary data are known, including the Ising, generalized Ising, canonical and full parameterizations. We also discuss a parameterization that we call the “spectral parameterization”, which has received significantly less coverage in existing ...

This paper presents a generalized method to implement the idea of parameterization and model realization to synthesize a control function that affects a possible state transfer that are equivalent to the controllability of the Linear Time-Invariant (LTI) control systems. The key idea here is that one should be able to link LTI control system with its system variables in parameterized form by th...

A new approach is proposed for stochastic parameterization of subgrid scale processes in models of atmospheric or oceanic circulation. The new approach relies on two key ingredients. First, the unresolved processes are represented by a Markov chain whose properties depend on the state of the resolved model variables. Second, the properties of this conditional Markov chain are inferred from data...

Parameterizations that use mesh simplification to build the base domain always adopt the vertex removal scheme. This paper applies edge collapse to constructing the base domain instead. After inducing the parameterization of the original mesh over the base domain, new algorithms map the new vertices in the simplified mesh back to the original one according to the edge transition sequence to int...

We show that the Flatté formula is not adequate to interpret precision data on a resonance production near an inelastic threshold. A unitary parameterization, satisfying generalized Watson’s theorem for the production amplitudes, is proposed to replace the Flatté parameterization in the phenomenological analyses of the experimental data.

This paper addresses the problem of computing planar patterns for compression garments. In the garment industry, the compression garment has been more and more widely used to retain a shape of human body, where certain strain (or normal pressure) is designed at some places on the compression garment. Variant values and distribution of strain can only be generated by sewing different 2D patterns...