arXiv subjects

Ge Chen

Publications and source records attributed to Ge Chen.

At least 55 records · Page 3Linked to original sources

arXiv2024

Deep Synoptic Array Science: Polarimetry of 25 New Fast Radio Bursts Provides Insights into their Origins

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.

astro-ph.HE↗

arXiv2024

On the Choice of Loss Function in Learning-based Optimal Power Flow

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.

eess.SY↗

arXiv2024

Multi-agent Modeling and Optimal Pumping Control of Magnetic Artificial Cilia

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.

math.OC↗

arXiv2023

Deep Synoptic Array Science: Implications of Faraday Rotation Measures of Localized Fast Radio Bursts

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.

astro-ph.HE↗

arXiv2023

Convergence Analysis and Strategy Control of Evolutionary Games with Imitation Rule on Toroidal Grid: A Full Version

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.

math.OC↗

arXiv2023

Evolutionary Games on Networks: Phase Transition, Quasi-equilibrium, and Mathematical Principles

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.

q-bio.PE↗

arXiv2023

Deep Synoptic Array science: A massive elliptical host among two galaxy-cluster fast radio bursts

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.

astro-ph.HE↗

arXiv2023

Deep Synoptic Array science: Two fast radio burst sources in massive galaxy clusters

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.

astro-ph.HE↗

arXiv2023

Deep Synoptic Array science: a 50 Mpc fast radio burst constrains the mass of the Milky Way circumgalactic medium

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.

astro-ph.GA↗

arXiv2022

Rethinking the Micro-Foundation of Opinion Dynamics: Rich Consequences of the Weighted-Median Mechanism

To identify the main mechanisms underlying complex opinion formation processes in social systems, researchers have long been exploring simple mechanistic mathematical models. Most existing opinion dynamics models are built on a common micro-foundation, i.e., the weighted-averaging opinion update. However, we argue that this universally-adopted mechanism features a non-negligible unrealistic feature, which brings unnecessary difficulties in seeking a proper balance between model complexity and predictive power. In this paper, we propose the weighted-median mechanism as a new micro-foundation of opinion dynamics, which, with minimal assumptions, fundamentally resolves the inherent unrealistic feature of the weighted-averaging mechanism. Derived from the cognitive dissonance theory in psychology, the weighted-median mechanism is supported by online experiment data and broadens the applicability of opinion dynamics models to multiple-choice issues with ordered discrete options. Moreover, the weighted-median mechanism, despite being the simplest in form, captures various non-trivial real-world features of opinion evolution, while some widely-studied averaging-based models fail to.

cs.SI↗

arXiv2022

Convergence, Consensus and Dissensus in the Weighted-Median Opinion Dynamics

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.

eess.SY↗

arXiv2022

Deep Synoptic Array science I: discovery of the host galaxy of FRB 20220912A

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.

astro-ph.HE↗

arXiv2022

Scheduling HVAC loads to promote renewable generation integration with a learning-based joint chance-constrained approach

The integration of distributed renewable generation (DRG) in distribution networks can be effectively promoted by scheduling flexible resources such as heating, ventilation, and air conditioning (HVAC) loads. However, finding the optimal scheduling for them is nontrivial because DRG outputs are highly uncertain. To address this issue, this paper proposes a learning-based joint chance-constrained approach to coordinate HVAC loads with DRG. Unlike cutting-edge works adopting individual chance constraints to manage uncertainties, this paper controls the violation probability of all critical constraints with joint chance constraints (JCCs). This joint manner can explicitly guarantee the operational security of the entire system based on operators' preferences. To overcome the intractability of JCCs, we first prove that JCCs can be safely approximated by robust constraints with proper uncertainty sets. A famous machine learning algorithm, one-class support vector clustering, is then introduced to construct a small enough polyhedron uncertainty set for these robust constraints. A linear robust counterpart is further developed based on the strong duality to ensure computational efficiency. Numerical results based on various distributed uncertainties confirm the advantages of the proposed method in optimality and feasibility.

eess.SY↗

arXiv2022

Efficient constraint learning for data-driven active distribution network operation

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.

math.OC↗

arXiv2022

Optimal Control for Unmanned Systems with One-way Broadcast Communication

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.

eess.SY↗

arXiv2022

Deep-quantile-regression-based surrogate model for joint chance-constrained optimal power flow with renewable generation

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.

math.OC↗

arXiv2022

Chance-constrained regulation capacity offering for HVAC systems under non-Gaussian uncertainties with mixture-model-based convexification

Heating, ventilation, and air-conditioning (HVAC) systems are ideal demand-side flexible resources to provide regulation services. However, finding the best hourly regulation capacity offers for HVAC systems in a power market ahead of time is challenging because they are affected by non-Gaussian uncertainties from regulation signals. Moreover, since HVAC systems need to frequently regulate their power according to regulation signals, numerous thermodynamic constraints are introduced, leading to a huge computational burden. This paper proposes a tractable chance-constrained model to address these challenges. It first develops a temporal compression approach, in which the extreme indoor temperatures in the operating hour are estimated and restricted in the comfortable range so that the numerous thermodynamic constraints can be compressed into only a few ones. Then, a novel convexification method is proposed to handle the non-Gaussian uncertainties. This method leverages the Gaussian mixture model to reformulate the chance constraints with non-Gaussian uncertainties on the left-hand side into deterministic non-convex forms. We further prove that these non-convex forms can be approximately convexified by second-order cone constraints with marginal optimality loss. Therefore, the proposed model can be efficiently solved with guaranteed optimality. Numerical experiments are conducted to validate the superiority of the proposed method.

math.OC↗

arXiv2022

Chance-constrained DC Optimal Power Flow with Non-Gaussian Distributed Uncertainties

Chance-constrained programming (CCP) is a promising approach to handle uncertainties in optimal power flow (OPF). However, conventional CCP usually assumes that uncertainties follow Gaussian distributions, which may not match reality. A few papers employed the Gaussian mixture model (GMM) to extend CCP to cases with non-Gaussian uncertainties, but they are only appropriate for cases with uncertainties on the right-hand side but not applicable to DC OPF that containing left-hand side uncertainties. To address this, we develop a tractable GMM-based chance-constrained DC OPF model. In this model, we not only leverage GMM to capture the probability characteristics of non-Gaussian distributed uncertainties, but also develop a linearization technique to reformulate the chance constraints with non-Gaussian distributed uncertainties on the left-hand side into tractable forms. A mathematical proof is further provided to demonstrate that the corresponding reformulation is a safe approximation of the original problem, which guarantees the feasibility of solutions.

math.OC↗