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The Deffuant-Weisbuch (DW) model is a well-known bounded-confidence opinion dynamics that has attracted wide interest. Although the heterogeneous DW model has been studied by simulations over $20$ years, its convergence proof is open. Our previous paper \cite{GC-WS-WM-FB:20} solves the problem for the case of uniform weighting factors greater than or equal to $1/2$, but the general case remains unresolved. This paper considers the DW model with heterogeneous confidence bounds and heterogeneous (unconstrained) weighting factors and shows that, with probability one, the opinion of each agent converges to a fixed vector. In other words, this paper resolves the convergence conjecture for the heterogeneous DW model. Our analysis also clarifies how the convergence speed may be arbitrarily slow under certain parameter conditions.

The Friedkin-Johnsen (FJ) model introduces prejudice into the opinion evolution and has been successfully validated in many practical scenarios; however, due to its weighted average mechanism, only one prejudiced agent can always guide all unprejudiced agents synchronizing to its prejudice under the connected influence network, which may not be in line with some social realities. To fundamentally address the limitation of the weighted average mechanism, a weighted-median opinion dynamics has been recently proposed; however, its theoretical analysis is challenging due to its nonlinear nature. This paper studies the weighted-median opinion dynamics with prejudice, and obtains the convergence and convergence rate when all agents have prejudice, and a necessary and sufficient condition for asymptotic consensus when a portion of agents have prejudice. These results are the first time to analyze the discrete-time and synchronous opinion dynamics with the weighted median mechanism, and address the phenomenon of the FJ model that connectivity leads to consensus when a few agents with the same prejudice join in an unprejudiced group.

The dynamic pricing of electricity is one of the most crucial demand response (DR) strategies in smart grid, where the utility company typically adjust electricity prices to influence user electricity demand. This paper models the relationship between the utility company and flexible electricity users as a Stackelberg game. Based on this model, we present a series of analytical results under certain conditions. First, we give an analytical Stackelberg equilibrium, namely the optimal pricing formula for utility company, as well as the unique and strict Nash equilibrium for users' electricity demand under this pricing scheme. To our best knowledge, it is the first optimal pricing formula in the research of price-based DR strategies. Also, if there exist prediction errors for the supply and demand of electricity, we provide an analytical expression for the energy supply cost of utility company. Moreover, a sufficient condition has been proposed that all electricity demands can be supplied by renewable energy. When the conditions for analytical results are not met, we provide a numerical solution algorithm for the Stackelberg equilibrium and verify its efficiency by simulation.

Graph autoencoders (GAEs), as a kind of generative self-supervised learning approach, have shown great potential in recent years. GAEs typically rely on distance-based criteria, such as mean-square-error (MSE), to reconstruct the input graph. However, relying solely on a single reconstruction criterion may lead to a loss of distinctiveness in the reconstructed graph, causing nodes to collapse into similar representations and resulting in sub-optimal performance. To address this issue, we have developed a simple yet effective strategy to preserve the necessary distinctness in the reconstructed graph. Inspired by the knowledge distillation technique, we found that the dual encoder-decoder architecture of GAEs can be viewed as a teacher-student relationship. Therefore, we propose transferring the knowledge of distinctness from the raw graph to the reconstructed graph, achieved through a simple KL constraint. Specifically, we compute pairwise node similarity scores in the raw graph and reconstructed graph. During the training process, the KL constraint is optimized alongside the reconstruction criterion. We conducted extensive experiments across three types of graph tasks, demonstrating the effectiveness and generality of our strategy. This indicates that the proposed approach can be employed as a plug-and-play method to avoid vague reconstructions and enhance overall performance.

Reinforcement Learning from Human Feedback (RLHF) facilitates the alignment of large language models (LLMs) with human preferences, thereby enhancing the quality of responses generated. A critical component of RLHF is the reward model, which is trained on preference data and outputs a scalar reward during the inference stage. However, the collection of preference data still lacks thorough investigation. Recent studies indicate that preference data is collected either by AI or humans, where chosen and rejected instances are identified among pairwise responses. We question whether this process effectively filters out noise and ensures sufficient diversity in collected data. To address these concerns, for the first time, we propose a comprehensive framework for preference data collection, decomposing the process into four incremental steps: Prompt Generation, Response Generation, Response Filtering, and Human Labeling. This structured approach ensures the collection of high-quality preferences while reducing reliance on human labor. We conducted comprehensive experiments based on the data collected at different stages, demonstrating the effectiveness of the proposed data collection method.

Opinion dynamics models are important in understanding and predicting opinion formation processes within social groups. Although the weighted-averaging opinion-update mechanism is widely adopted as the micro-foundation of opinion dynamics, it bears a non-negligibly unrealistic implication: opinion attractiveness increases with opinion distance. Recently, the weighted-median mechanism has been proposed as a new microscopic mechanism of opinion exchange. Numerous advancements have been achieved regarding this new micro-foundation, from theoretical analysis to empirical validation, in a discrete-time asynchronous setup. However, the original discrete-time weighted-median model does not allow for "compromise behavior" in opinion exchanges, i.e., no intermediate opinions are created between disagreeing agents. To resolve this problem, this paper propose a novel continuous-time weighted-median opinion dynamics model, in which agents' opinions move towards the weighted-medians of their out-neighbors' opinions. It turns out that the proof methods for the original discrete-time asynchronous model are no longer applicable to the analysis of the continuous-time model. In this paper, we first establish the existence and uniqueness of the solution to the continuous-time weighted-median opinion dynamics by showing that the weighted-median mapping is contractive on any graph. We also characterize the set of all the equilibria. Then, by leveraging a new LaSalle invariance principle argument, we prove the convergence of the continuous-time weighted-median model for any initial condition and derive a necessary and sufficient condition for the convergence to consensus., Comment: 13 pages, 1 figure

Graphs are ubiquitous in real-world scenarios and encompass a diverse range of tasks, from node-, edge-, and graph-level tasks to transfer learning. However, designing specific tasks for each type of graph data is often costly and lacks generalizability. Recent endeavors under the "Pre-training + Fine-tuning" or "Pre-training + Prompt" paradigms aim to design a unified framework capable of generalizing across multiple graph tasks. Among these, graph autoencoders (GAEs), generative self-supervised models, have demonstrated their potential in effectively addressing various graph tasks. Nevertheless, these methods typically employ multi-stage training and require adaptive designs, which on one hand make it difficult to be seamlessly applied to diverse graph tasks and on the other hand overlook the negative impact caused by discrepancies in task objectives between the different stages. To address these challenges, we propose GA^2E, a unified adversarially masked autoencoder capable of addressing the above challenges seamlessly. Specifically, GA^2E proposes to use the subgraph as the meta-structure, which remains consistent across all graph tasks (ranging from node-, edge-, and graph-level to transfer learning) and all stages (both during training and inference). Further, GA^2E operates in a \textbf{"Generate then Discriminate"} manner. It leverages the masked GAE to reconstruct the input subgraph whilst treating it as a generator to compel the reconstructed graphs resemble the input subgraph. Furthermore, GA^2E introduces an auxiliary discriminator to discern the authenticity between the reconstructed (generated) subgraph and the input subgraph, thus ensuring the robustness of the graph representation through adversarial training mechanisms. We validate GA^2E's capabilities through extensive experiments on 21 datasets across four types of graph tasks.

The static properties and dynamic evolution of bottomonium states in a hot QCD medium are investigated through the Schr\"odinger equation with complex heavy quark potentials, which are presented recently in lattice QCD study and with three different extractions. This approach builds a direct connection between the in-medium heavy quark potentials from the lattice QCD to the experimental observables. The yields and nuclear modification factors $R_{AA}$ of bottomonium in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=5.02~\rm TeV$ are calculated in this work. Our results show a large suppression of the bottomonium yield in heavy ion collisions due to the large imaginary potential. To understand bottomonium $R_{AA}$ based on lattice QCD potentials, we propose a fomration time for bottomonium states and find that experimental data can be well explained with the heavy quark potential extracted by the Pad\'e fit, which shows no color screening in the real part potential., Comment: 7 pages, 9 figures

We analyze and contrast two ways to train machine learning models for solving AC optimal power flow (OPF) problems, distinguished with the loss functions used. The first trains a mapping from the loads to the optimal dispatch decisions, utilizing mean square error (MSE) between predicted and optimal dispatch decisions as the loss function. The other intends to learn the same mapping, but directly uses the OPF cost of the predicted decisions, referred to as decision loss, as the loss function. In addition to better aligning with the OPF cost which results in reduced suboptimality, the use of decision loss can circumvent feasibility issues that arise with MSE when the underlying mapping from loads to optimal dispatch is discontinuous. Since decision loss does not capture the OPF constraints, we further develop a neural network with a specific structure and introduce a modified training algorithm incorporating Lagrangian duality to improve feasibility.} This result in an improved performance measured by feasibility and suboptimality as demonstrated with an IEEE 39-bus case study., Comment: 5 pages, Accepted by PESGM2024

Risk limiting dispatch (RLD) has been proposed as an approach that effectively trades off economic costs with operational risks for power dispatch under uncertainty. However, how to solve the RLD problem with provably near-optimal performance still remains an open problem. This paper presents a learning-based solution to this challenge. We first design a data-driven formulation for the RLD problem, which aims to construct a decision rule that directly maps day-ahead observable information to cost-effective dispatch decisions for the future delivery interval. Unlike most existing works that follow a predict-then-optimize paradigm, this end-to-end rule bypasses the additional suboptimality introduced by separately handling prediction and optimization. We then propose neural RLD, a novel solution method to the data-driven formulation. This method leverages an L2-regularized neural network to learn the decision rule, thereby transforming the data-driven formulation into a neural network training task that can be efficiently completed by stochastic gradient descent. A theoretical performance guarantee is further established to bound the suboptimality of our method, which implies that its suboptimality approaches to zero with high probability as more samples are utilized. Simulation tests across various systems demonstrate our method's superior performance in convergence, suboptimality, and computational efficiency compared with benchmarks., Comment: 10 pages

Tiny cilia drive the flow of surrounding fluids through asymmetric jumping, which is one of the main ways for biological organisms to control fluid transport at the micro-scale. Due to its huge application prospects in medical and environmental treatment fields, artificial cilia have attracted widespread research interest in recent years. However, how to model and optimize artificial cilia is currently a common challenge faced by scholars. We model a single artificial cilium driven by a magnetic field as a multi-agent system, where each agent is a magnetic bead, and the interactions between beads are influenced by the magnetic field. Our system is driven by controlling the magnetic field input to achieve fluid transport at low Reynolds number. In order to quantify the flow conveying capacity, we introduce the pumping performance and propose an optimal control problem for pumping performance, and then give its numerical solution. The calculation results indicate that our model and optimal control algorithm can significantly improve the pumping performance of a single cilia.

Graph contrastive learning (GCL) has emerged as a representative graph self-supervised method, achieving significant success. The currently prevalent optimization objective for GCL is InfoNCE. Typically, it employs augmentation techniques to obtain two views, where a node in one view acts as the anchor, the corresponding node in the other view serves as the positive sample, and all other nodes are regarded as negative samples. The goal is to minimize the distance between the anchor node and positive samples and maximize the distance to negative samples. However, due to the lack of label information during training, InfoNCE inevitably treats samples from the same class as negative samples, leading to the issue of false negative samples. This can impair the learned node representations and subsequently hinder performance in downstream tasks. While numerous methods have been proposed to mitigate the impact of false negatives, they still face various challenges. For instance, while increasing the number of negative samples can dilute the impact of false negatives, it concurrently increases computational burden. Thus, we propose GraphRank, a simple yet efficient graph contrastive learning method that addresses the problem of false negative samples by redefining the concept of negative samples to a certain extent, thereby avoiding the issue of false negative samples. The effectiveness of GraphRank is empirically validated through experiments on the node, edge, and graph level tasks.

Heavy ion collisions provide a unique opportunity for studying the properties of exotic hadrons with two charm quarks. The production of $T_{cc}^+$ is significantly enhanced in nuclear collisions compared to proton-proton collisions due to the creation of multiple charm pairs. In this study, we employ the Langevin equation in combination with the Instantaneous Coalescence Model (LICM) to investigate the production of $T_{cc}^+$ and $\Xi_{cc}^{++}$ which consists of two charm quarks. We consider $T_{cc}^+$ as molecular states composed of $D$ and $D^*$ mesons. The Langevin equation is used to calculate the energy loss of charm quarks and $D$ mesons in the hot medium. The hadronization process, where charm quarks transform into each $D$ state as constituents of $T_{cc}^+$ production, is described using the coalescence model. The coalescence probability between $D$ and $D^*$ is determined by the Wigner function, which encodes the information of the $T_{cc}^+$ wave function. Our results show that the $T_{cc}^+$ production varies by approximately one order of magnitude when different widths in the Wigner function, representing distinct binding energies of $T_{cc}^+$, are considered. This variation offers valuable insights into the nature of $T_{cc}^+$ through the analysis of its wave function. The $\Xi_{cc}^{++}$ is treated as a hadronic state produced at the hadronization of the deconfined matter. Its production is also calculated as a comparison with the molecular state $T_{cc}^+$., Comment: 8 pages, 5 figures

We report on a full-polarization analysis of the first 25 as yet non-repeating FRBs detected at 1.4 GHz by the 110-antenna Deep Synoptic Array (DSA-110) during commissioning observations. We present details of the data-reduction, calibration, and analysis procedures developed for this novel instrument. Faraday rotation measures (RMs) are searched between $\pm10^6$ rad m$^{-2}$ and detected for 20 FRBs with magnitudes ranging from $4-4670$ rad m$^{-2}$. $15/25$ FRBs are consistent with 100% polarization, 10 of which have high ($\ge70\%$) linear-polarization fractions and 2 of which have high ($\ge30\%$) circular-polarization fractions. Our results disfavor multipath RM scattering as a dominant depolarization mechanism. Polarization-state and possible RM variations are observed in the four FRBs with multiple sub-components. We combine the DSA-110 sample with polarimetry of previously published FRBs, and compare the polarization properties of FRB sub-populations and FRBs with Galactic pulsars. Although FRB polarization fractions are typically higher than those of Galactic pulsars, and cover a wider range than those of pulsar single pulses, they resemble those of the youngest (characteristic ages $<10^{5}$ yr) pulsars. Our results support a scenario wherein FRB emission is intrinsically highly linearly polarized, and propagation effects can result in conversion to circular polarization and depolarization. Young pulsar emission and magnetospheric-propagation geometries may form a useful analogy for the origin of FRB polarization., Comment: 57 pages, 24 figures, 5 tables ; version accepted by ApJ ; revised classification to include polarized signal-to-noise; added appendices for PA error/variability, J1935 polarization ; corrected literature FRB sample and supplemented with omitted data; added discussion of biases, limitations, and selection criteria; revised sigmaRM analysis ; additional plots added ; revised FRB20220424E analysis

Faraday rotation measures (RMs) of fast radio bursts (FRBs) offer the prospect of directly measuring extragalactic magnetic fields. We present an analysis of the RMs of ten as yet non-repeating FRBs detected and localized to host galaxies by the 110-antenna Deep Synoptic Array (DSA-110). We combine this sample with published RMs of 15 localized FRBs, nine of which are repeating sources. For each FRB in the combined sample, we estimate the host-galaxy dispersion measure (DM) contributions and extragalactic RM. We find compelling evidence that the extragalactic components of FRB RMs are often dominated by contributions from the host-galaxy interstellar medium (ISM). Specifically, we find that both repeating and as yet non-repeating FRBs show a correlation between the host-DM and host-RM in the rest frame, and we find an anti-correlation between extragalactic RM (in the observer frame) and redshift for non-repeaters, as expected if the magnetized plasma is in the host galaxy. Important exceptions to the ISM origin include a dense, magnetized circum-burst medium in some repeating FRBs, and the intra-cluster medium (ICM) of host or intervening galaxy clusters. We find that the estimated ISM magnetic-field strengths, $\bar{B}_{||}$, are characteristically larger than those inferred from Galactic radio pulsars. This suggests either increased ISM magnetization in FRB hosts in comparison with the Milky Way, or that FRBs preferentially reside in regions of increased magnetic-field strength within their hosts., Comment: 13 pages, 4 figures, 1 table ; added references to section 1, 2, and 3; added a paragraph in Section 3 to discuss simulations addressing interplay of local and ISM magnetic field; added bar to B|| to indicate average over line of sight

This paper investigates discrete-time evolutionary games with a general stochastic imitation rule on the toroidal grid, which is a grid network with periodic boundary conditions. The imitation rule has been considered as a fundamental rule to the field of evolutionary game theory, while the grid is treated as the most basic network and has been widely used in the research of spatial (or networked) evolutionary games. However, currently the investigation of evolutionary games on grids mainly uses simulations or approximation methods, while few strict analysis is carried out on one-dimensional grids. This paper proves the convergence of evolutionary prisoner's dilemma, evolutionary snowdrift game, and evolutionary stag hunt game with the imitation rule on the two-dimensional grid, for the first time to our best knowledge. Simulations show that our results may almost reach the critical convergence condition for the evolutionary snowdrift (or hawk-dove, chicken) game. Also, this paper provides some theoretical results for the strategy control of evolutionary games, and solves the Minimum Agent Consensus Control (MACC) problem under some parameter conditions. We show that for some evolutionary games (like the evolutionary prisoner's dilemma) on the toroidal grid, one fixed defection node can drive all nodes almost surely converging to defection, while at least four fixed cooperation nodes are required to lead all nodes almost surely converging to cooperation.

The stable cooperation ratio of spatial evolutionary games has been widely studied using simulations or approximate analysis methods. However, sometimes such ``stable'' cooperation ratios obtained via approximate methods might not be actually stable, but correspond to quasi-equilibriums instead. We find that various classic game models, like the evolutionary snowdrift game, evolutionary prisoner's dilemma, and spatial public goods game on square lattices and scale-free networks, exhibit the phase transition in convergence time to the equilibrium state. Moreover, mathematical principles are provided to explain the phase transition of convergence time and quasi-equilibrium of cooperation ratio. The findings explain why and when cooperation and defection have a long-term coexistence., Comment: 11 pages, 7 figures

The hot gas that constitutes the intracluster medium (ICM) has been studied at X-ray and millimeter/sub-millimeter wavelengths (Sunyaev-Zeldovich effect) for decades. Fast radio bursts (FRBs) offer an additional method of directly measuring the ICM and gas surrounding clusters, via observables such as dispersion measure (DM) and Faraday rotation measure (RM). We report the discovery of two FRB sources detected with the Deep Synoptic Array (DSA-110) whose host galaxies belong to massive galaxy clusters. In both cases, the FRBs exhibit excess extragalactic DM, some of which likely originates in the ICM of their respective clusters. FRB 20220914A resides in the galaxy cluster Abell 2310 at z=0.1125 with a projected offset from the cluster center of 520 kpc. The host of a second source, FRB 20220509G, is an elliptical galaxy at z=0.0894 that belongs to the galaxy cluster Abell 2311 at projected offset of 870 kpc. These sources represent the first time an FRB has been localized to a galaxy cluster. We combine our FRB data with archival X-ray, SZ, and optical observations of these clusters in order to infer properties of the ICM, including a measurement of gas temperature from DM and ySZ of 0.8-3.9 keV. We then compare our results to massive cluster halos from the IllustrisTNG simulation. Finally, we describe how large samples of localized FRBs from future surveys will constrain the ICM, particularly beyond the virial radius of clusters.

The stellar population environments associated with fast radio burst (FRB) sources provide important insights for developing their progenitor theories. We expand the diversity of known FRB host environments by reporting two FRBs in massive galaxy clusters discovered by the Deep Synoptic Array (DSA-110) during its commissioning observations. FRB 20220914A has been localized to a star-forming, late-type galaxy at a redshift of 0.1139 with multiple starbursts at lookback times less than $\sim$3.5 Gyr in the Abell 2310 galaxy cluster. Although the host galaxy of FRB 20220914A is similar to typical FRB hosts, the FRB 20220509G host stands out as a quiescent, early-type galaxy at a redshift of 0.0894 in the Abell 2311 galaxy cluster. The discovery of FRBs in both late and early-type galaxies adds to the body of evidence that the FRB sources have multiple formation channels. Therefore, even though FRB hosts are typically star-forming, there must exist formation channels consistent with old stellar population in galaxies. The varied star formation histories of the two FRB hosts we report indicate a wide delay-time distribution of FRB progenitors. Future work in constraining the FRB delay-time distribution, using methods we develop herein, will prove crucial in determining the evolutionary histories of FRB sources., Comment: 18 pages, 9 figures

We present the Deep Synoptic Array (DSA-110) discovery and interferometric localization of the so far non-repeating FRB 20220319D. The FRB originates in a young, rapidly star-forming barred spiral galaxy, IRAS 02044$+$7048, at just 50 Mpc. Although the NE2001 and YMW16 models for the Galactic interstellar-medium (ISM) contribution to the DM of FRB 20220319D exceed its total observed DM, we show that uncertainties in these models accommodate an extragalactic origin for the burst. We derive a conservative upper limit on the DM contributed by the circumgalactic medium (CGM) of the Milky Way: the limit is either 28.7 pc cm$^{-3}$ and 47.3 pc cm$^{-3}$, depending on which of two pulsars nearby on the sky to FRB 20220319D is used to estimate the ISM DM. These limits both imply that the total Galactic CGM mass is $<10^{11}M_{\odot}$, and that the baryonic mass of the Milky Way is $\lesssim60\%$ of the cosmological average given the total halo mass. More stringent albeit less conservative constraints are possible when the DMs of pulsars in the distant globular cluster M53 are additionally considered. Although our constraints are sensitive to possible anisotropy in the CGM and to the assumed form of the radial-density profile, they are not subject to uncertainties in the chemical and thermal properties of the CGM. Our results strongly support scenarios commonly predicted by galaxy-formation simulations wherein feedback processes expel baryonic matter from the halos of galaxies like the Milky Way., Comment: 17 pages, 8 figures, 3 tables, submitted to AAS Journals

Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated via experimental data. Numerical studies also indicate that this new mechanism recreates some non-trivial real-world features of opinion evolution. In this paper, we conduct a thorough theoretical analysis of the weighted-median opinion dynamics. We fully characterize the set of all equilibria, and we establish the almost-sure finite-time convergence for any initial condition. Moreover, we prove a necessary and sufficient graph-theoretic condition for the almost-sure convergence to consensus, as well as a sufficient graph-theoretic condition for almost-sure persistent dissensus. It turns out that the weighted-median opinion dynamics, despite its simplicity in form, exhibit rich dynamical behavior that depends on some delicate network structures. To complement our sufficient conditions for almost-sure dissensus, we further prove that, given the influence network, determining whether the system almost surely achieves persistent dissensus is NP-hard, which reflects the complexity the network topology contributes to opinion evolution.

We report the detection and interferometric localization of the repeating fast radio burst (FRB) source FRB 20220912A during commissioning observations with the Deep Synoptic Array (DSA-110). Two bursts were detected from FRB 20220912A, one each on 2022 October 18 and 2022 October 25. The best-fit position is (R.A. J2000, decl. J2000) = (23:09:04.9, +48:42:25.4), with a 90% confidence error ellipse of $\pm2$ arcsec and $\pm1$ arcsec in right ascension and declination respectively. The two bursts have disparate polarization properties and temporal profiles. We find a Faraday rotation measure that is consistent with the low value of $+0.6$ rad m$^{-2}$ reported by CHIME/FRB. The DSA-110 localization overlaps with the galaxy PSO J347.2702+48.7066 at a redshift $z=0.0771$, which we identify as the likely host. PSO J347.2702$+$48.7066 has a stellar mass of approximately $10^{10}M_{\odot}$, modest internal dust extinction, and a star-formation rate likely in excess of $0.1\,M_{\odot}$ yr$^{-1}$. The host-galaxy contribution to the dispersion measure is likely $\lesssim50$ pc cm$^{-3}$. The FRB 20220912A source is therefore likely viewed along a tenuous plasma column through the host galaxy., Comment: 10 pages, 7 figures, 2 tables, submitted to AAS Journals

Scheduling flexible sources to promote the integration of renewable generation is one fundamental problem for operating active distribution networks (ADNs). However, existing works are usually based on power flow models, which require network parameters (e.g., topology and line impedance) that may be unavailable in practice. To address this issue, we propose an efficient constraint learning method to operate ADNs. This method first trains multilayer perceptrons (MLPs) based on historical data to learn the mappings from decisions to constraint violations and power loss. Then, power flow constraints can be replicated by these MLPs without network parameters. We further prove that MLPs learn constraints by formulating a union of disjoint polytopes to approximate the corresponding feasible region. Thus, the proposed method can be interpreted as a piecewise linearization method, which also explains its desirable ability to replicate complex constraints. Finally, a two-step simplification method is developed to reduce its computational burden. The first step prunes away unnecessary polytopes from the union above. The second step drops redundant linear constraints for each retained polytope. Numerical experiments based on the IEEE 33- and 123-bus test systems validate that the proposed method can achieve desirable optimality and feasibility simultaneously with guaranteed computational efficiency., Comment: 10 pages

Unmanned systems (USs) including unmanned aerial vehicles, unmanned underwater vehicles, and unmanned ground vehicles have great application prospects in military and civil fields, among which the process of finding feasible and optimal paths for the agents in USs is a kernel problem. Traditional path finding algorithms are hard to adequately obtain optimal paths in real-time under fast time-varying and poor communication environments. We propose an online optimal control algorithm for USs based on a one-way broadcast communication mode under the assumption of a poor communication environment, mobile targets, radars (or sonar), and missiles (or torpedoes). With the principle of receding horizon control, optimal (or suboptimal) paths are then generated by the approximation theory of neural networks and gradient optimization techniques, with low computation requirements. Also, we give a convergence analysis for our algorithm, and show that each agent can reach its target in finite time under some conditions on agents, targets and radar-missiles. Moreover, simulations demonstrate that the agents in USs can generate optimal (or suboptimal) paths in real time using our algorithm while effectively avoiding collision with other agents or detection by enemy radars.

Joint chance-constrained optimal power flow (JCC-OPF) is a promising tool to manage uncertainties from distributed renewable generation. However, most existing works are based on power flow equations, which require accurate network parameters that may be unobservable in many distribution systems. To address this issue, this paper proposes a learning-based surrogate model for JCC-OPF with renewable generation. This model equivalently converts joint chance constraints in quantile-based forms and introduces deep quantile regression to replicate them, in which a multi-layer perceptron (MLP) is trained with a special loss function to predict the quantile of constraint violations. Another MLP is trained to predict the expected power loss. Then, the JCC-OPF can be formulated without network parameters by reformulating these two MLPs into mixed-integer linear constraints. To further improve its performance, two pre-processing steps, i.e., data augmentation and calibration, are developed. The former trains a simulator to generate more training samples for enhancing the prediction accuracy of MLPs. The latter designs a positive parameter to calibrate the predictions of MLPs so that the feasibility of solutions can be guaranteed. Numerical experiments based on the IEEE 33- and 123-bus systems validate that the proposed model can achieve desirable feasibility and optimality simultaneously with no need for network parameters., Comment: 10 pages