Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments

Superconductivity and Non-Classical Long-Range Order on a Quantum Computer

An important problem in quantum information is the practical demonstration of non-classical long-range order on quantum computers. One of the best known examples of a quantum system with non-classical long-range order is a superconductor. Here we achieve Cooper pairing of qubits on a quantum computer to represent superconducting or superfluid states. We rigorously confirm the quantum long-range order by measuring the large $O(N)$ eigenvalue of the two-electron reduced density matrix. The demonstration of maximal quantum long-range order is an important step towards more complex modeling of superconductivity and superfluidity as well as other phenomena with significant quantum long-range order on quantum computers

Quantum Simulation of Bosons with the Contracted Quantum Eigensolver

Quantum computers are promising tools for simulating many-body quantum systems due to their potential scaling advantage over classical computers. While significant effort has been expended on many-fermion systems, here we simulate a model entangled many-boson system with the contracted quantum eigensolver (CQE). We generalize the CQE to many-boson systems by encoding the bosonic wavefunction on qubits. The CQE provides a compact ansatz for the bosonic wave function whose gradient is proportional to the residual of a contracted Schr\"odinger equation. We apply the CQE to a bosonic system, where $N$ quantum harmonic oscillators are coupled through a pairwise quadratic repulsion. The model is relevant to the study of coupled vibrations in molecular systems on quantum devices. Results demonstrate the potential efficiency of the CQE in simulating bosonic processes such as molecular vibrations with good accuracy and convergence even in the presence of noise

Bench vs. Jury Trials Convictions and Sentencing Outcomes for Arrested Officers, 2005-2016

Presentation at the Annual Meeting of the Academy of Criminal Justice Sciences, Las Vegas, NV, on March 18, 2022

No equity, no triple aim: strategic proposals to advance health equity in a volatile policy environment

Health professionals, including social workers, community health workers, public health workers, and licensed health care providers, share common interests and responsibilities in promoting health equity and improving social determinants of health—the conditions in which we live, work, play, and learn. This article summarizes underlying causes of health inequity and comparatively poor health outcomes in the U.S. It describes barriers to realizing the hope embedded in the 2010 Patient Protection and Affordable Care Act that moving away from fee-for-service payments will naturally drive care upstream as providers respond to greater financial risk for the health of their patients by undertaking greater prevention efforts. The article asserts that health equity should serve as the guiding framework for achieving the Triple Aim of health care reform. It outlines practical opportunities for improving care and for promoting stronger efforts to address social determinants of health. These proposals include developing a dashboard of measures to assist providers committed to health equity and community-based prevention and to promote institutional accountability for addressing socio-economic factors that influence health

No equity, no triple aim: strategic proposals to advance health equity in a volatile policy environment

Health professionals, including social workers, community health workers, public health workers, and licensed health care providers, share common interests and responsibilities in promoting health equity and improving social determinants of health—the conditions in which we live, work, play, and learn. This article summarizes underlying causes of health inequity and comparatively poor health outcomes in the U.S. It describes barriers to realizing the hope embedded in the 2010 Patient Protection and Affordable Care Act that moving away from fee-for-service payments will naturally drive care upstream as providers respond to greater financial risk for the health of their patients by undertaking greater prevention efforts. The article asserts that health equity should serve as the guiding framework for achieving the Triple Aim of health care reform. It outlines practical opportunities for improving care and for promoting stronger efforts to address social determinants of health. These proposals include developing a dashboard of measures to assist providers committed to health equity and community-based prevention and to promote institutional accountability for addressing socio-economic factors that influence health