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   https://doi.org/10.23919/ACC45564.2020.9147847  

   Caluya, Kenneth F.; Halder, Abhishek (July 2020, Proceedings of the 2020 American Control Conference)

   null (Ed.)

   In this paper, we study the feedback synthesis problem for steering the joint state density or ensemble subject to multi-input state feedback linearizable dynamics. This problem is of interest to many practical applications including that of dynamically shaping a robotic swarm. Our results here show that it is possible to exploit the structural nonlinearities to derive the feedback controllers steering the joint density from a prescribed shape to another while minimizing the expected control effort to do so. The developments herein build on our previous work, and extend the theory of the Schrödinger bridge problem subject to feedback linearizable dynamics. 

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   The QMol-grid package provides a suite of routines for performing quantum-mechanical simulations in atomic and molecular systems, currently implemented in one spatial dimension. It supports ground- and excited-state calculations for the Schrödinger equation, density-functional theory, and Hartree–Fock levels of theory as well as propagators for field-free and field-driven time-dependent Schrödinger equation (TDSE) and real-time time-dependent density-functional theory (TDDFT), using symplectic-split schemes. The package is written using MATLAB’s object-oriented features and handle classes. It is designed to facilitate access to the wave function(s) (TDSE) and the Kohn–Sham orbitals (TDDFT) within MATLAB’s environment. 

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3. Computing time-periodic steady-state currents via the time evolution of tensor network states

   https://doi.org/10.1063/5.0099741  

   Strand, Nils E.; Vroylandt, Hadrien; Gingrich, Todd R. (August 2022, The Journal of Chemical Physics)

   We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a lattice with periodic boundary conditions subject to a time-periodic drive, can be stochastically evolved in time to sample representative trajectories via a Gillespie method. In lieu of generating realizations of trajectories, a BTTN state can variationally approximate a distribution over the vast number of many-body configurations. We apply the density matrix renormalization group algorithm to initialize BTTN states, which are then propagated in time via the time-dependent variational principle (TDVP) algorithm to yield the steady-state behavior, including the effects of both typical and rare trajectories. The application of the methods to ratchet currents is highlighted, but the approach extends naturally to other interacting lattice models with time-dependent driving. Although trajectory sampling is conceptually and computationally simpler, we discuss situations for which the BTTN TDVP strategy can be beneficial. 

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4. Exploring algorithmic fairness in robust graph covering problems

   Rahmattalabi, A. (January 2019, Advances in Neural Information Processing Systems)

   Fueled by algorithmic advances, AI algorithms are increasingly being deployed in settings subject to unanticipated challenges with complex social effects. Motivated by real-world deployment of AI driven, social-network based suicide prevention and landslide risk management interventions, this paper focuses on a robust graph covering problem subject to group fairness constraints. We show that, in the absence of fairness constraints, state-of-the-art algorithms for the robust graph covering problem result in biased node coverage: they tend to discriminate individuals (nodes) based on membership in traditionally marginalized groups. To remediate this issue, we propose a novel formulation of the robust covering problem with fairness constraints and a tractable approximation scheme applicable to real world instances. We provide a formal analysis of the price of group fairness (PoF) for this problem, where we show that uncertainty can lead to greater PoF. We demonstrate the effectiveness of our approach on several real-world social networks. Our method yields competitive node coverage while significantly improving group fairness relative to state-of-the-art methods. 

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5. Finite Horizon Density Steering for Multi-input State Feedback Linearizable Systems

   Caluya, Kenneth F. (January 2020, 2020 American Control Conference.)

   In this paper, we study the feedback synthesis problem for steering the joint state density or ensemble subject to multi-input state feedback linearizable dynamics. This problem is of interest to many practical applications including that of dynamically shaping a robotic swarm. Our results here show that it is possible to exploit the structural nonlinearities to derive the feedback controllers steering the joint density from a prescribed shape to another while minimizing the expected control effort to do so. The developments herein build on our previous work, and extend the theory of the Schro ̈dinger bridge problem subject to feedback linearizable dynamics. 

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