Noisy atomic magnetometry in real time

Continuously monitored atomic spin-ensembles allow, in principle, for real-time sensing of external magnetic fields beyond classical limits. Within the linear-Gaussian regime, thanks to the phenomenon of measurement-induced spin-squeezing, they attain a quantum-enhanced scaling of sensitivity both as a function of time, t, and the number of atoms involved, N. In our work, we rigorously study how such conclusions based on Kalman filtering methods change when inevitable imperfections are taken into account: in the form of collective noise, as well as stochastic fluctuations of the field in time. We prove that even an infinitesimal amount of noise disallows the error to be arbitrarily diminished by simply increasing N, and forces it to eventually follow a classical-like behaviour in t. However, we also demonstrate that, "thanks" to the presence of noise, in most regimes the model based on a homodyne-like continuous measurement actually achieves the ultimate sensitivity allowed by the decoherence, yielding then the optimal quantum-enhancement. We are able to do so by constructing a noise-induced lower bound on the error that stems from a general method of classically simulating a noisy quantum evolution, during which the stochastic parameter to be estimated—here, the magnetic field—is encoded. The method naturally extends to schemes beyond the linear-Gaussian regime, in particular, also to ones involving feedback or active control.

Oscillations Governed by the Incoherent Dynamics in Necroptotic Signaling

Emerging evidences have suggested that oscillation is important for the induction of cell death. However, whether and how oscillation behavior is involved and required for necroptosis remain elusive. To address this question, a minimal necroptotic circuit is proposed based on the CNS pathway. Stochastic parameter analysis demonstrates that the essential structure for oscillation of the CNS circuit is constituted by a paradoxical component embedded with positive feedback among the three protein nodes, i.e., RIP1, caspase-8, and RIP3. Distribution characteristics of all parameters in the CNS circuit with stable oscillation are investigated as well, and a unidirectional bias with fast and slow dynamics that are required for high occurrence probability of oscillation is identified. Four types of oscillation behaviors are classified and their robustness is further explored, implying that the fast oscillation behavior is more robust than the slow behavior. In addition, bifurcation analysis and landscape approach are employed to study stochastic dynamics and global stability of the circuit oscillations, revealing the possible switching strategies among different behaviors. Taken together, our study provides a natural and physical bases for understanding the occurrence of oscillations in the necroptotic network, advancing our knowledge of oscillations in regulating the various cell death signaling.

Adaptive event-triggered distributed recursive filtering with stochastic parameters and faults

This paper investigates the distributed recursive filtering issue of a class of stochastic parameter systems with randomly occurring faults. An event-triggered scheme with an adaptive threshold is designed to better reduce the communication load by considering dynamic changes of measurement sequences. In the framework of Kalman filtering, a distributed filter is constructed to simultaneously estimate both system states and faults. Then, the upper bound of filtering error covariance is derived with the help of stochastic analysis combined with basis matrix inequalities. The obtained condition with a recursive feature is dependent on the statistical characteristic of stochastic parameter matrices as well as the time-varying threshold. Furthermore, the desired filter gain is derived by minimizing the trace of the obtained upper bound. Finally, two simulation examples are conducted to demonstrate the effectiveness and feasibility of the proposed filtering method.

Output-based Event-triggered Control of Networked Systems Subject to Bilateral Packet Dropouts

In this paper, an output-based event-triggered control problem of discrete-time networked control systems (NCSs) subject to bilateral data packet dropouts is investigated. In view of the stochastic sequences of packet dropouts in measurement channels (from sensors to controller) and control channels (from controller to actuators), the NCS is converted into a closed-loop stochastic parameter system. In the aid of a Lyapunov functional based on stochastic variables, sufficient conditions on co-design of event-triggering strategy and exponentially mean-square stability of NCSs are derived. Furthermore, an improved iterative algorithm is given to obtain the dynamic output feedback control law and event-triggering parameters from the nonconvex inequalities. Finally, a numerical example and the corresponding simulation results are given to show the validity and applicability of the developed techniques.

A Progress Report on the Development of the High-Resolution Rapid Refresh Ensemble

The High-Resolution Rapid Refresh Ensemble (HRRRE) is a 36-member ensemble analysis system with nine forecast members that utilizes the Advanced Research Weather Research and Forecasting (ARW-WRF) dynamic core and the physics suite from the operational Rapid Refresh/High-Resolution Rapid Refresh deterministic modeling system. A goal of HRRRE development is a system with sufficient spread amongst members, comparable in magnitude to the random error in the ensemble mean, to represent the range of possible future atmospheric states. HRRRE member diversity has traditionally been obtained by perturbing the initial and lateral boundary conditions of each member, but recent development has focused on implementing stochastic approaches in HRRRE to generate additional spread. These techniques were tested in retrospective experiments and in the May 2019 Hazardous Weather Testbed Spring Experiment (HWT-SE). Results show a 6–25% increase in the ensemble spread in 2-m temperature, 2-m mixing ratio, and 10-m wind speed when stochastic parameter perturbations are used in HRRRE (HRRRE-SPP). Case studies from HWT-SE demonstrate that HRRRE-SPP performed similar to or better than the operational High-Resolution Ensemble Forecast system version 2 (HREFv2) and the non-stochastic HRRRE. However, subjective evaluations provided by HWT-SE forecasters indicated that overall, HRRRE-SPP predicted lower probabilities of severe weather (using updraft helicity as a proxy) compared to HREFv2. A statistical analysis of the performance of HRRRE-SPP and HREFv2 from the 2019 summer convective season supports this claim, but also demonstrates that the two systems have similar reliability for prediction of severe weather using updraft helicity.

Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule

Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters, using feedback from measurements performed on the quantum device. Here we study the problem of estimating the gradient of the function to be optimized directly from quantum measurements, generalizing and simplifying some approaches present in the literature, such as the so-called parameter-shift rule. We derive a mathematically exact formula that provides a stochastic algorithm for estimating the gradient of any multi-qubit parametric quantum evolution, without the introduction of ancillary qubits or the use of Hamiltonian simulation techniques. The gradient measurement is possible when the underlying device can realize all Pauli rotations in the expansion of the Hamiltonian whose coefficients depend on the parameter. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy, for instance due to the coupling between the quantum device and an unknown environment.