Sequential Update Research Articles

Integration of machine learning and process‐based model outputs via ensemble Kalman filter enhanced space–time modelling of soil organic carbon in a highly human impacted area

AbstractAccurate prediction of soil organic carbon stock (SOCS) dynamics in areas with intensive human activities is crucial for developing sustainable soil management practices and climate change mitigation strategies. This study investigated the spatiotemporal dynamics of SOCS by collecting a total of 1219 topsoil samples in southern Jiangsu Province of China in 1980, 2000 and 2015, and compared the performance of three predictive models: random forest (RF), RothC, and a hybrid model of RF‐RothCEnKF. The hybrid model integrated outputs from the process‐based RothC model and the data‐driven RF model using the Ensemble Kalman Filter (EnKF) for sequential model state updates. Results showed that the three models presented similar spatial patterns of SOCS from 1980 to 2015, with relatively higher SOCS mainly distributed in the areas surrounding Taihu Lake. The mean SOCS change rates estimated by the RF‐RothCEnKF model represented an overall net increase of 0.04 t C ha−1 yr.−1 during that period. The RF‐RothCEnKF model exhibited high prediction accuracy, with an R2 of .52, a mean absolute error (MAE) of 7.38 t C ha−1, and a root mean square error (RMSE) of 9.13 t C ha−1 in 2015. This highlighted the RF‐RothCEnKF's ability to enhance performance when the individual RF model (R2 = .47, MAE = 7.66 t C ha−1, and RMSE = 9.42 t C ha−1) and the RothC (R2 = .13, MAE = 8.77 t C ha−1, and RMSE = 10.87 t C ha−1) fell short. Our findings may not only provide a framework for integrating process‐based and machine learning models to enhance the accuracy and adaptability of SOCS modelling in areas affected by intensive human activities, but also offer some guidance for developing sustainable agricultural practices and carbon management strategies in complex environmental settings.

Negative results on density determination with one-dimensional cellular automata with block-sequential asynchronous updates

A large number of research efforts have been made in trying to solve global decision problems with cellular automata by means of their cells reaching a distributed consensus via their local action. Among them, the determination of the most frequent state in configurations with arbitrary size, i.e., the density classification task, has been the most widely approached benchmark problem. The literature abounds with cases demonstrating that, depending on how it is formulated, a solution can be shown to exist or not. Here we address the problem in terms of deterministic, block-sequential asynchronous updates, over cyclic configurations, by which the possibility of a solution remains open. Our main results are negative in terms of the possibility of solving the problem with such formulation, encompassing the cases of any cellular automaton with any sequential update, and any elementary cellular automaton with any block-sequential update; furthermore, we uncover some properties that any potential solution with block-sequential update should have in order for it to be a candidate to solving the problem. Incidentally, we also give a new, very simple proof of the impossibility of solving the problem with any synchronous rule.

An Obstacle Avoidance Trajectory Planning Methodology Based on Energy Minimization (OTPEM) for the Tilt-Wing eVTOL in the Takeoff Phase

Electric tilt-wing flying cars are an efficient, economical, and environmentally friendly solution to urban traffic congestion and travel efficiency issues. This article addresses the high energy consumption and obstacle interference during the takeoff phase of the tilt-wing eVTOL (electric Vertical Takeoff and Landing), proposing a trajectory planning method based on energy minimization and obstacle avoidance. Firstly, based on the dynamics analysis, the relationship between energy consumption, spatial trajectory, and obstacles is sorted out and the decision variables for the trajectory planning problem with obstacle avoidance are determined. Secondly, based on the power discretization during the takeoff phase, the energy minimization objective function is established and the constraints of performance limitations and spatial obstacles are derived. Thirdly, by integrating the optimization model with the SLSQP (Sequential Least Squares Quadratic Programming algorithm), the second-order sequential quadratic programming model and decision variable update equations are derived, establishing the solution process for the trajectory planning problem of the tilt-wing eVTOL takeoff with obstacle avoidance. Finally, the Airbus Vahana A3 is taken as an example to verify and validate the effectiveness, stability, and robustness of the model and optimization algorithm proposed. The validation results show that the OTPEM (obstacle avoidance trajectory planning methodology based on energy minimization) can effectively handle changes in the takeoff end state and exhibits good stability and robustness in different obstacle environments. It can provide a certain reference for the three-dimensional obstacle avoidance trajectory planning of Airbus Vahana A3 and other tilt-wing eVTOL trajectory planning problems.

Optimistic sequential multi-agent reinforcement learning with motivational communication

Centralized Training with Decentralized Execution (CTDE) is a prevalent paradigm in the field of fully cooperative Multi-Agent Reinforcement Learning (MARL). Existing algorithms often encounter two major problems: independent strategies tend to underestimate the potential value of actions, leading to the convergence on sub-optimal Nash Equilibria (NE); some communication paradigms introduce added complexity to the learning process, complicating the focus on the essential elements of the messages. To address these challenges, we propose a novel method called Optimistic Sequential Soft Actor Critic with Motivational Communication (OSSMC). The key idea of OSSMC is to utilize a greedy-driven approach to explore the potential value of individual policies, named optimistic Q-values, which serve as an upper bound for the Q-value of the current policy. We then integrate a sequential update mechanism with optimistic Q-value for agents, aiming to ensure monotonic improvement in the joint policy optimization process. Moreover, we establish motivational communication modules for each agent to disseminate motivational messages to promote cooperative behaviors. Finally, we employ a value regularization strategy from the Soft Actor Critic (SAC) method to maximize entropy and improve exploration capabilities. The performance of OSSMC was rigorously evaluated against a series of challenging benchmark sets. Empirical results demonstrate that OSSMC not only surpasses current baseline algorithms but also exhibits a more rapid convergence rate.

Development of a time pressure-based model for the simulation of an evacuation in a fire emergency

The study of pedestrian behaviour in a fire emergency is essential for effectively reducing the number of casualties. However, most studies only consider the effect of fire on pedestrian behaviour and ignore the effect of a fire emergency on pedestrian psychology. In this study, we introduce a method of assessing the pedestrian time pressure within a cellular automaton model using the available safe egress time and required safe egress time in fire evacuations. Moreover, a more realistic reflection of the evacuation process in a fire emergency is obtained by introducing Pyrosim to compute the fire floor field and by proposing a sequential update method based on time pressure. To assess the model, we conduct sensitivity analyses on model parameters across various environmental configurations. Numerical simulation results show that fire accelerates the evacuation rate and radiated heat transfer and temperature have the greatest effects on the time pressure of pedestrians in a fire evacuation. The distribution of pedestrians is U-shaped owing to fire avoidance behaviour and in the later stage of evacuation, pedestrians keeping away from heated walls. The trend of time pressure over time has a bimodal distribution as pedestrians initially pass the fire and the environment then becomes untenable as the fire fully develops. In addition, the exit location affects the evacuation process, with a symmetrical positioning improving the evacuation efficiency. We verify the model in a series of physical experiments. The agreement between the numerical simulation results and experimental results demonstrates that the time pressure-based model is suitable for simulating the route choice behaviour and evacuation process in fire emergencies.

Application of coastal acoustic tomography: calibration of open boundary conditions on a numerical ocean model for tidal currents

Coastal acoustic tomography (CAT), which measures path-averaged currents from reciprocal acoustic transmission experiments and reconstructs velocity fields from the multiple path-averaged current data, is useful for monitoring tidal currents in coastal shallow water, especially if data assimilation is employed. Previous CAT data assimilation studies have focused on state estimation problems, i.e., the reconstruction of tidal currents and following dynamical discussion. In this study, we investigate the use of path-averaged currents in a boundary control problem. Specifically, we aim to use the observed path-averaged currents to determine the parameters of a numerical ocean model, which were tidal amplitudes and phases as the open boundary conditions in this study. We investigate two methods: using the ensemble Kalman filter (EnKF) results and a linearization approach called model Green’s function method. Both calibration methods decreased the amplitudes of tidal constituents at the open boundaries. We compare the model performance between the model predictions with and without the calibration of the open boundary conditions. The model predictions with the calibrated open boundary conditions improved the agreement with the observed path-averaged current. We also implemented the sequential updates of EnKF with the two calibrated open boundary conditions. The EnKF results with the independently calibrated two open boundary conditions improved the agreement with the comparison data obtained by acoustic Doppler current profiler measurement compared with the original EnKF result with the initial open boundary conditions.

Gaussian Mixture Probability Hypothesis Density Filter for Heterogeneous Multi-Sensor Registration

Spatial registration is a prerequisite for data fusion. Existing methods primarily focus on similar sensor scenarios and rely on accurate data association assumptions. To address the heterogeneous sensor registration in complex data association scenarios, this paper proposes a Gaussian mixture probability hypothesis density (GM-PHD)-based algorithm for heterogeneous sensor bias registration, accompanied by an adaptive measurement iterative update algorithm. Firstly, by constructing augmented target state motion and measurement models, a closed-form expression for prediction is derived based on Gaussian mixture (GM). In the subsequent update, a two-level Kalman filter is used to achieve an approximate decoupled estimation of the target state and measurement bias, taking into account the coupling between them through pseudo-likelihood. Notably, for heterogeneous sensors that cannot directly use sequential update techniques, sequential updates are first performed on sensors that can obtain complete measurements, followed by filtering updates using extended Kalman filter (EKF) sequential update techniques for incomplete measurements. When there are differences in sensor quality, the GM-PHD fusion filter based on measurement iteration update is sequence-sensitive. Therefore, the optimal subpattern assignment (OSPA) metric is used to optimize the fusion order and enhance registration performance. The proposed algorithms extend the multi-target information-based spatial registration algorithm to heterogeneous sensor scenarios and address the impact of different sensor-filtering orders on registration performance. Our proposed algorithms significantly improve the accuracy of bias estimation compared to the registration algorithm based on significant targets. Under different detection probabilities and clutter intensities, the average root mean square error (RMSE) of distance and angular biases decreased by 11.8% and 8.6%, respectively.

Toward interpretable LSTM-based modeling of hydrological systems

Abstract. Several studies have demonstrated the ability of long short-term memory (LSTM) machine-learning-based modeling to outperform traditional spatially lumped process-based modeling approaches for streamflow prediction. However, due mainly to the structural complexity of the LSTM network (which includes gating operations and sequential processing of the data), difficulties can arise when interpreting the internal processes and weights in the model. Here, we propose and test a modification of LSTM architecture that is calibrated in a manner that is analogous to a hydrological system. Our architecture, called “HydroLSTM”, simulates the sequential updating of the Markovian storage while the gating operation has access to historical information. Specifically, we modify how data are fed to the new representation to facilitate simultaneous access to past lagged inputs and consolidated information, which explicitly acknowledges the importance of trends and patterns in the data. We compare the performance of the HydroLSTM and LSTM architectures using data from 10 hydro-climatically varied catchments. We further examine how the new architecture exploits the information in lagged inputs, for 588 catchments across the USA. The HydroLSTM-based models require fewer cell states to obtain similar performance to their LSTM-based counterparts. Further, the weight patterns associated with lagged input variables are interpretable and consistent with regional hydroclimatic characteristics (snowmelt-dominated, recent rainfall-dominated, and historical rainfall-dominated). These findings illustrate how the hydrological interpretability of LSTM-based models can be enhanced by appropriate architectural modifications that are physically and conceptually consistent with our understanding of the system.

Predicting rock mass rating ahead of the tunnel face with Bayesian estimation

The rock mass rating (RMR) system plays a crucial role in geomechanics assessments for tunnel projects. However, conventional methods combining empirical and geostatistical approaches often yield inaccuracies, particularly in areas with weak strata such as faults and karst caves. To address these uncertainties and errors inherent in empirical techniques, we propose a progressive RMR prediction strategy based on the Bayesian framework. This strategy incorporates three key components: 1) Variogram modeling: utilizing observational data from the excavation face, we construct and update a variogram model to capture the spatial variability of RMR. 2) TSP-RMR statistic model: we integrate a TSP-RMR statistical model into the Bayesian sequential update process. 3) Bayesian maximum entropy (BME) integration: the BME method combines geological information obtained from tunnel surface excavation with tunnel seismic prediction (TSP) data, ultimately enhancing the RMR prediction accuracy. Our methodology is applied to the Laoying rock tunneling project in Yunnan Province, China. Our findings demonstrate that the fusion of soft data and geological interpretation significantly improves the accuracy of RMR predictions. At selected prediction points, the relative error of our method is less than 15% when compared to the traditional Kriging method. This approach holds substantial potential for advancing RMR estimation ahead of tunnel excavation, particularly when advanced geological forecast data are available.

Vibration monitoring of structures with indirect load identification and Kalman update

The German Research Foundation (DFG) has launched in September 2022 the priority program SPP 2388 100+ to develop new methods for digital representation, SHM and lifetime management of complex structures, due to the continuously increasing amount of old infrastructure buildings. The present contribution is prepared within the LEMOTRA project as a part of SPP 2388 100+. Among various SHM methods, the approach based on the Kalman update for data assimilation between model and measurement is applied and further developed to create a kind of functional digital twin for SHM. For this purpose, a sound numerical model and a measurement system with a continuous data flow are introduced to provide online predictions of the state and response parameters of the structure. System changes resulting from damage or aging processes can be detected and localized, provided the measurement and the model prediction deal with the same cause. Thus, the load identification is a necessary prerequisite for reliable data assimilation techniques. A two-step update procedure is proposed and applied in this context. At first, one part of the measurement system is used for the load identification. A cluster structure of convolutional neural networks (CNNs) was developed, trained and calibrated to extract load characteristics such as load magnitudes, load velocities or the number of vehicles on the bridge from multiple acceleration signals. This information is then used to reconstruct the actual load. In the second step, a different set of sensors is used for the data assimilation. In contrast to the first set of measurement locations, the measurement data from these sensors should be sensitive to potential system changes or damage. Here, the identified load is used as input for the model predictions which are then compared to the measurement data. A combination of different ensemble based Kalman filters (KF) provides a sequential update of the state parameters (e.g. displacement, velocity, acceleration) and the model parameters (e.g. stiffness, mass, damping). The cluster CNN approach is tested numerically, and the data assimilation technique is tested on a laboratory structure.

Enhancing Collaboration in Heterogeneous Multiagent Systems Through Communication Complementary Graph.

Heterogeneous multiagent systems are characterized by diverse task distributions, which are prevalent in practical scenarios, such as distributed decision making and robotic collaboration. A significant challenge in these systems is the constraint of limited observations, where each agent has access only to partial information. Many studies facilitate information exchange by employing shared parameters among agents. However, this approach is generally more effective for homogeneous systems where agents have similar observation or action spaces. In heterogeneous systems, indiscriminate parameter sharing can significantly increase the exploration cost required for effective adaptation. To address this challenge, we propose a novel communication complementary graph model (CCGM) for enhancing collaboration in heterogeneous multiagent systems. Our approach builds upon the training framework of heterogeneous agent reinforcement learning (HARL) with trust region learning and nonparameter sharing. This model utilizes advantage function decomposition and sequential updates to promote policy convergence. Within this framework, we introduce a novel communication method inspired by signaling games, where agents acting as receivers, process messages from other agents alongside their own observations. CCGM aligns the messages with observations in a graph-based communication module, which establishes communication relationships and supplements observational information. Subsequently, agents generate self-interested information, which they then share with others as senders. We evaluate our algorithm across various environments, including multiagent particle environments (MPE) and multiagent MuJoCo (MAMuJoCo) robot experiments. The results demonstrate the effectiveness of CCGM in enhancing HARL-based algorithms.

Multilayer Online Sequential Reduced Kernel Extreme Learning Machine-Based Modeling for Time-Varying Distributed Parameter Systems.

A significant number of industrial dynamic processes belong to time-varying distributed parameter systems (DPSs). To develop an accurate approximation model for these systems, it is critical to capture their time-varying behavior and strong nonlinearity. In this article, a multilayer online sequential reduced kernel extreme learning machine (ML-OSRKELM)-based online spatiotemporal modeling approach is developed for such DPSs. First, ML-OSRKELM stacks multiple online sequential reduced kernel extreme learning machine autoencoders (OSRKELM-AEs) to create a deep network, which can translate the spatiotemporal domain into a low-dimensional time domain. Then, an online sequential reduced kernel extreme learning machine (OS-RKELM) is employed to construct a dynamic temporal model. Finally, after obtaining time coefficients from the time domain, OS-RKELM is also used to reconstruct the original spatiotemporal domain. By using the kernel trick and the support vector selection strategy, the proposed method can remove redundant information while maintaining satisfactory nonlinear learning performance. Furthermore, the designed sequential update scheme can update the model parameters with real-time data, which makes it a promising method for capturing time-varying dynamics. Experiments and simulations on a lithium-ion battery's thermal process confirm the excellent performance and validity of the proposed model.

Reducing rejection exponentially improves Markov chain Monte Carlo sampling

The choice of transition kernel critically influences the performance of the Markov chain Monte Carlo method. Despite the importance of kernel choice, guiding principles for optimal kernels have not been established. Here, we propose a one-parameter rejection control transition kernel that can be applied to various Monte Carlo samplings and demonstrate that the rejection process plays a major role in determining the sampling efficiency. Varying the rejection probability, we examine the autocorrelation time of the order parameter in the two- and three-dimensional ferromagnetic Potts models. Our results reveal that reducing the rejection rate leads to an exponential decrease in autocorrelation time in sequential spin updates and an algebraic reduction in random spin updates. The autocorrelation times of conventional algorithms almost fall on a single curve as a function of the rejection rate. The present transition kernel with an optimal parameter provides one of the most efficient samplers for general cases of discrete variables.

Joint Base Station and IRS Deployment for Enhancing Network Coverage: A Graph-Based Modeling and Optimization Approach

Intelligent reflecting surface (IRS) can be densely deployed in complex environment to create cascaded line-of-sight (LoS) paths between multiple base stations (BSs) and users via tunable IRS reflections, thereby significantly enhancing the coverage performance of wireless networks. To achieve this goal, it is vital to optimize the deployed locations of BSs and IRSs in the wireless network, which is investigated in this paper. Specifically, we divide the coverage area of the network into multiple non-overlapping cells and decide whether to deploy a BS/IRS in each cell given a total number of BSs/IRSs available. We show that to ensure the network coverage/communication performance, i.e., each cell has a direct/cascaded LoS path with at least one BS, as well as such LoS paths have the average number of IRS reflections less than a given threshold, there is a fundamental trade-off with the deployment cost or the number of BSs/IRSs needed. To optimally characterize this trade-off, we formulate a joint BS and IRS deployment problem based on graph theory, which, however, is difficult to be optimally solved due to the combinatorial optimization involved. To circumvent this difficulty, we first consider a simplified problem with given BS deployment and propose the optimal as well as an efficient suboptimal IRS deployment solution to it, by applying the branch-and-bound method and iteratively removing IRSs from the candidate locations, respectively. Next, an efficient sequential update algorithm is proposed for solving the joint BS and IRS deployment problem. Numerical results are provided to show the efficacy of the proposed design approach and optimization algorithms for the joint BS and IRS deployment. The trade-off between the network coverage performance and the number of deployed BSs/IRSs with different cost ratios is also unveiled.

Research on Timing Sequence Update Strategy Decision of Project Portfolio Based on Coupling Benefits in Strategic Period

The Chinese government’s substantial investment in water restoration has created numerous lucrative opportunities for commercial environmental restoration enterprises. Accordingly, this research study seeks to address the primary challenge faced by enterprise managers: selecting projects that fulfill both strategic imperatives and maximize economic returns. To tackle this issue, we segmented the overarching strategic period into multiple phases and studied the project portfolio from a holistic strategic period perspective. We introduced a decision model for the dynamic, sequential updating of the portfolio throughout the strategic period, emphasizing the combined benefits at each phase. This model guides the strategic selection of projects at any decision-making stage to optimize the benefits across the entire strategic duration. The multi-agent Nash Q-learning algorithm was employed for portfolio construction and updating strategies. This approach yields an optimal project portfolio for each phase of the strategy. Unlike traditional methods that predominantly focus on cumulative returns and find it challenging to accommodate strategic shifts, our proposed technique prioritizes intertwined strategic returns. It promotes project choices in tune with strategic contexts and supports ongoing adjustments to project strategies, providing invaluable guidance for decision makers. A comparison of our proposed method with other optimization strategies validated its superior performance. Furthermore, the case study described in this study confirms that our method promotes project choices in tune with strategic contexts and supports ongoing adjustments to project strategies, providing invaluable guidance for decision makers.

Identifying generalizable equilibrium pricing strategies for charging service providers in coupled power and transportation networks

Transportation electrification, involving large-scale integration of electric vehicles (EV) and fast charging stations (FCS), plays a critical role for global energy transition and decarbonization. In this context, coordination of EV routing and charging activities through suitably designed price signals constitutes an imperative step in secure and economic operation of the coupled power-transportation networks (CPTN). This work examines the non-cooperative pricing competition between self-interested EV charging service providers (CSP), taken into account the complex interactions between CSPs' pricing strategies, EV users' decisions and the operation of CPTN. The modeling of CPTN environment captures the prominent type of uncertainties stemming from the gasoline vehicle and EV origin-destination travel demands and their cost elasticity, EV initial state-of-charge and renewable energy sources (RES). An enhanced multi-agent proximal policy optimization method is developed to solve the pricing game, which incorporates an attention mechanism to selectively incorporate agents' representative information to mitigate the environmental non-stationarity without raising dimensionality challenge, while safeguarding the commercial confidentiality of CSP agents. To foster more efficient learning coordination in the highly uncertain CPTN environment, a sequential update scheme is also developed to achieve monotonic policy improvement for CSP agents. Case studies on an illustrative and a large-scale test system reveal that the proposed method facilitates sufficient competition among CSP agents and corroborates the core benefits in terms of reduced charging costs for EV users, enhancement of RES absorption and cost efficiency of the power distribution network. Results also validate the excellent generalization capability of the proposed method in coping with CPTN uncertainties. Finally, the rationale of the proposed attention mechanism is validated and the superior computational performance is highlighted against the state-of-the-art methods.

Bayesian evidence synthesis for informative hypotheses: An introduction.

To establish a theory one needs cleverly designed and well-executed studies with appropriate and correctly interpreted statistical analyses. Equally important, one also needs replications of such studies and a way to combine the results of several replications into an accumulated state of knowledge. An approach that provides an appropriate and powerful analysis for studies targeting prespecified theories is the use of Bayesian informative hypothesis testing. An additional advantage of the use of this Bayesian approach is that combining the results from multiple studies is straightforward. In this article, we discuss the behavior of Bayes factors in the context of evaluating informative hypotheses with multiple studies. By using simple models and (partly) analytical solutions, we introduce and evaluate Bayesian evidence synthesis (BES) and compare its results to Bayesian sequential updating. By doing so, we clarify how different replications or updating questions can be evaluated. In addition, we illustrate BES with two simulations, in which multiple studies are generated to resemble conceptual replications. The studies in these simulations are too heterogeneous to be aggregated with conventional research synthesis methods. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Sensor Management with Dynamic Clustering for Bearings-Only Multi-Target Tracking via Swarm Intelligence Optimization

Sensor management is a crucial research subject for multi-sensor multi-target tracking in wireless sensor networks (WSNs) with limited resources. Bearings-only tracking produces further challenges related to high nonlinearity and poor observability. Moreover, energy efficiency and energy balancing should be considered for sensor management in WSNs, which involves networking and transmission. This paper formulates the sensor management problem in the partially observable Markov decision process (POMDP) framework and uses the cardinality-balanced multi-target multi-Bernoulli (CBMeMBer) filter for tracking. A threshold control method is presented to reduce the impact on tracking accuracy when using bearings-only measurements for sequential update. Moreover, a Cauchy–Schwarz divergence center is defined to construct a new objective function for efficiently finding the optimal sensor subset via swarm intelligence optimization. This is also conducive to dynamic clustering for the energy efficiency and energy balancing of the network. The simulation results illustrate that the proposed solution can achieve good tracking performance with less energy, and especially that it can effectively balance network energy consumption and prolong network lifetime.

Optimized emulation of quantum magnetometry via superconducting qubits

Quantum magnetometry based on adaptive phase estimation allows for Heisenberg precision while avoiding creation and maintenance of complex entangled states. However, the absolute sensitivity is limited by the nonoptimal use of quantum resources provided by multiple-qubit devices and algorithmic realizations of the protocol. Here, addressing both issues, we advance the time-ascending phase estimation protocol by numerical improvements of Bayesian learning, i.e., sequential updating of the field distribution, and optimal exploitation of resources provided by unentangled qubits with limited coherence. Such algorithmic improvements are used to evaluate the absolute sensitivity both on a simulator and by pulsed-transmon experiments conducted on the IBMQ platform, where we take advantage of high coherence time. In addition, we compare the proficiency of separable and entangled states for magnetometry and show that, in practice, separable states provide superior performance. Flux-sensing emulation experiments demonstrate that a sensitivity of $(0.17--1.74)\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}\phantom{\rule{4pt}{0ex}}{(\sqrt{\mathrm{Hz}})}^{\ensuremath{-}1}$ (where ${\mathrm{\ensuremath{\Phi}}}_{0}$ is the flux quantum) for a single-qubit magnetometer and $(0.06--0.65)\ensuremath{\mu}{\mathrm{\ensuremath{\Phi}}}_{0}\phantom{\rule{4pt}{0ex}}{(\sqrt{\mathrm{Hz}})}^{\ensuremath{-}1}$ for a five-qubit magnetometer can be achieved for slowly oscillating $1--10\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$ magnetic fields, which is comparable to more established experimental platforms for magnetometry.

Coalition Formation Game for Cost-Efficient Multiparty Payment Channel in Payment Channel Networks.

Blockchain has introduced a new era for online payment services and its economy with tamper-proof cryptocurrencies. However, blockchain, which is based on global peer-to-peer networks, has its limitations due to payment delays from global consensus and transaction costs for maintenance. Thus, payment channel networks (PCN) have been proposed as one of the most promising off-chain solutions, allowing users to pay directly through payment channels (PC), with minimal blockchain involvement. However, payment delays and cost problems still exist, especially given the large size of the PCN. This study proposes a multiparty payment channel (MPC) that enables multiple users to join the same PC and exchange payment transactions, compared to the legacy PC. To avoid a consensus procedure among users in the PC, we introduce sequential and parallel updates for the PC status. Since increasing the MPC size limits the advantages in terms of the delay and cost, we propose a distributed coalition formation algorithm to form the MPC group, in which each user has the choice to join or leave the group. Simulations show that the proposed algorithm establishes MPCs successfully, considering the trade-off between the payoff gain and the MPC delay cost.