BZPEERReading, trust and collaboration for researchDiscover
Workspaces
Network
Opportunities
Account
Researcher profile
Xudong Chen contributes to research discovery and scholarly infrastructure.
Trust snapshot
Actions
Identity and collaboration
Claiming links this public author record to a researcher profile and unlocks direct collaboration workflows.
Log in to claimDirect collaboration
Claim this author entity first to unlock direct invitations.
Research graph
Inspect adjacent work, topics, institutions and collaborators without jumping out to a separate graph page.
BZPEER is loading the nearby papers, people, topics and institutions for this page.
Published work
A step-graphon has the strong (resp., weak) $H$-property if a directed, random graph sampled from it has a Hamilton cycle (resp., a node-wise disjoint cycle cover) asymptotically almost surely. The weak/strong $H$-property is essentially a zero-one property. We identify key objects associated with the step-graphon that matter for the zero-one law and provide a complete characterization.
Large language models (LLMs) have become a strong foundation for multi-agent systems, but their effectiveness depends heavily on orchestration design. Across different tasks, role design, capacity assignment, and dependency construction jointly affect both solution quality and execution efficiency. Existing approaches automate parts of this design process, yet they often optimize these decisions partially or sequentially, and rely on execution-level feedback that provides limited credit assignment for local orchestration decisions. We propose LEMON (\textbf{L}earning \textbf{E}xecutable \textbf{M}ulti-agent \textbf{O}rchestratio\textbf{N} via Counterfactual Reinforcement Learning), an LLM-based orchestrator that generates an executable orchestration specification. The specification integrates task-specific roles, customized duties, capacity levels, and dependency structure into a single deployable system. To train the orchestrator, we augment the orchestration-level GRPO objective with a localized counterfactual signal that edits role, capacity, or dependency fields and applies the resulting reward contrast only to the edited spans. Experiments on six reasoning and coding benchmarks, including MMLU, GSM8K, AQuA, MultiArith, SVAMP, and HumanEval, show that LEMON achieves state-of-the-art performance among the evaluated multi-agent orchestration methods. Our code is available at https://anonymous.4open.science/r/LEMON-B23C.
We provide in this paper a sufficient condition for a polynomial dynamical system $\dot x(t) = f(x(t))$ to be super-linearizable, i.e., to be such that all its trajectories are linear projections of the trajectories of a linear dynamical system. The condition is expressed in terms of the hereby introduced weighted dependency graph $G$, whose nodes $v_i$ correspond to variables $x_i$ and edges $v_iv_j$ have weights $\frac{\partial f_j}{\partial x_i}$. We show that if the product of the edge weights along any cycle in $G$ is a constant, then the system is super-linearizable. The proof is constructive, and we provide an algorithm to obtain super-linearizations and illustrate it on an example.
In this paper, we propose a novel stochastic binary resetting algorithm for networks of pulse-coupled oscillators (or, simply, agents) to reach global synchronization. The algorithm is simple to state: Every agent in a network oscillates at a common frequency. Upon completing an oscillation, an agent generates a Bernoulli random variable to decide whether it sends pulses to all of its out-neighbors or it stays quiet. Upon receiving a pulse, an agent resets its state by following a binary phase update rule. We show that such an algorithm can guarantee global synchronization of the agents almost surely as long as the underlying information flow topology is a rooted directed graph. The proof of the result relies on the use of a stochastic hybrid dynamical system approach. Toward the end of the paper, we present numerical demonstrations for the validity of the result and, also, numerical studies about the times needed to reach synchronization for various information flow topologies.
We address an open problem in ensemble control: Whether there exist controllable linear ensemble systems over multi-dimensional parameterization spaces? We provide a negative result: Any real-analytic linear ensemble system is not $\mathrm{L}^p$-controllable, for $2\leq p \leq \infty$, if its parameterization space contains an open set in $\mathbb{R}^d$ for $d \geq 2$.
The demand of probabilistic time series forecasting has been recently raised in various dynamic system scenarios, for example, system identification and prognostic and health management of machines. To this end, we combine the advances in both deep generative models and state space model (SSM) to come up with a novel, data-driven deep probabilistic sequence model. Specifically, we follow the popular encoder-decoder generative structure to build the recurrent neural networks (RNN) assisted variational sequence model on an augmented recurrent input space, which could induce rich stochastic sequence dependency. Besides, in order to alleviate the inconsistency issue of the posterior between training and predicting as well as improving the mining of dynamic patterns, we (i) propose using a lagged hybrid output as input for the posterior at next time step, which brings training and predicting into alignment; and (ii) further devise a generalized auto-regressive strategy that encodes all the historical dependencies for the posterior. Thereafter, we first investigate the methodological characteristics of the proposed deep probabilistic sequence model on toy cases, and then comprehensively demonstrate the superiority of our model against existing deep probabilistic SSM models through extensive numerical experiments on eight system identification benchmarks from various dynamic systems. Finally, we apply our sequence model to a real-world centrifugal compressor forecasting problem, and again verify its outstanding performance by quantifying the time series predictive distribution.
In a recent paper arXiv:2109.08340, we have exhibited a set of conditions that are necessary for the $H$-property to hold for the class of step-graphons. In this paper, we prove that these conditions are essentially sufficient.
Light scattering within scattering media presents a substantial obstacle to optical transmission. A speckle pattern with random amplitude and phase distribution is observed when coherent light travels through strong scattering media. Fortunately, wavefront shaping has been successfully employed with a spatial light modulator to recover intensity targets after scattering media, such as a sharp focus point or specified two-dimensional patterns. There have, however, been few studies that attempted to separately manipulate the amplitude and phase of the focusing field. In this paper, we propose a feedback-based wavefront shaping method to generate complex optical fields through scattering medium. A reliable phase retrieval approach is introduced to provide the complex feedback information, i.e., the amplitude and phase of the focusing field. Accordingly, in order to modulate the speckle field into a desired complex structured optical field, a multi-objective genetic algorithm is used to find the best phase map. To demonstrate the proposed method's high performance, experimental tests have been carried out. High fidelity is demonstrated in the generation of diverse complex light fields, both in amplitude and phase. Our findings may facilitate the manipulation of light field through scattering medium, and are anticipated to further promote future applications such as optogenetics, vortex optical communication, and optical trapping through scattering media.
We explore in this paper sufficient conditions for the $H$-property to hold, with a particular focus on the so-called line graphons. A graphon is a symmetric, measurable function from the unit square $[0,1]^2$ to the closed interval $[0,1]$. Graphons can be used to sample random graphs, and a graphon is said to have the $H$-property if graphs on $n$ nodes sampled from it admit a node-cover by disjoint cycles -- such a cover is called a Hamiltonian decomposition -- almost surely as $n \to \infty$. A step-graphon is a graphon which is piecewise constant over rectangles in the domain. To a step-graphon, we assign two objects: its concentration vector, encoding the areas of the rectangles, and its skeleton-graph, describing their supports. These two objects were used in our earlier work [3] to establish necessary conditions for a step-graphon to have the $H$-property. In this paper, we prove that these conditions are essentially also sufficient for the class of line-graphons, i.e., the step-graphons whose skeleton graphs are line graphs with a self-loop at an ending node. We also investigate borderline cases where neither the necessary nor the sufficient conditions are met.
By utilizing tools from game theory, we develop a novel multi-period-multi-company demand response framework considering the interactions between companies (sellers of energy) and their consumers (buyers of energy). We model the interactions in terms of a Stackelberg game, where companies set their prices and consumers respond by choosing their demands. We show that the underlying game has a unique equilibrium at which the companies maximize their revenues while the consumers maximize their utilities subject to their local constraints. Closed-form expressions are provided for the optimal strategies of all players. Based on these solutions, a power allocation game has been formulated, which is shown to admit a unique pure-strategy Nash equilibrium, for which closed-form expressions are also provided. This equilibrium is found under the assumption that companies can freely allocate their power across the time horizon, but we also demonstrate that it is possible to relax this assumption. We further provide a fast distributed algorithm for the computation of all optimal strategies using only local information. We also study the effect of variations in the number of periods (subdivisions of the time horizon) and the number of consumers. As a consequence, we are able to find an appropriate company-to-consumer ratio when the number of consumers participating in demand response exceeds some threshold. Furthermore, we show, both analytically and numerically, that the multi-period scheme provides incentives for energy consumers to participate in demand response, compared to the single-period framework studied in the literature. In our framework, we provide a condition for the minimum budgets consumers need, and carry out case studies using real life data to demonstrate the benefits of the approach, which show potential savings of up to $30\%$ and equilibrium prices that have low volatility.
We call a finite, spanning set of a semi-simple real Lie algebra a distinguished set if it satisfies the following property: The Lie bracket of any two elements out of the set is, up to some constant, another element in the set; conversely, for any element in the set, there are two elements out of the set whose Lie bracket is, up to some constant, the given element. We show in the paper that every semi-simple real Lie algebra has a distinguished set.
We introduce in the paper a novel observability problem for a continuum ensemble of nonholonomic control systems with unknown population density. We address the problem by focussing on a prototype of such ensemble system, namely, the ensemble of Bloch equations. The dynamics of the equations are structurally identical, but show variations in Larmor dispersion and radio frequency (rf) inhomogeneity. We assume that the initial state of every individual system is unknown and, moreover, the population density of these individual systems is also unknown. Furthermore, we assume that at any time, there is only one scalar measurement output at our disposal. The measurement output integrates a certain observation function, common to all individual systems, over the continuum ensemble. The observability problem we pose in the paper is thus the following: Whether one is able to use the common control input (i.e., the rf field) and the single measurement output to estimate the initial states of the individual systems and, moreover, to identify the population density? Amongst other things, we establish a sufficient condition for the ensemble system to be observable: We show that if the common observation function is any harmonic homogeneous polynomial of positive degree, then the ensemble system is observable. The main focus of the paper is to demonstrate how to leverage tools from representation theory of Lie algebras to address the observability problem. Although the results we establish in the paper are for the specific ensemble of Bloch equations, the approach we develop along the analysis can be generalized to investigate observability of other general ensembles of nonholonomic control systems with a single, integrated measurement output.
In this paper, we study the problem of robust global synchronization of resetting clocks in multi-agent networked systems, where by robust global synchronization we mean synchronization that is insensitive to arbitrarily small disturbances, and which is achieved from all initial conditions. In particular, we aim to address the following question: Given a set of homogeneous agents with periodic clocks sharing the same parameters, what kind of information flow topologies will guarantee that the resulting networked systems can achieve robust global synchronization? To address this question, we rely on the framework of robust hybrid dynamical systems and a class of distributed hybrid resetting algorithms. Using the hybrid-system approach, we provide a partial solution to the question: Specifically, we show that one can achieve robust global synchronization with no purely discrete-time solutions in any networked system whose underlying information flow topology is a rooted acyclic digraph. Such a result is complementary to the existing result [1] in which strongly connected digraphs are considered as the underlying information flow topologies of the networked systems. We have further computed in the paper the convergence time for a networked system to reach global synchronization. In particular, the computation reveals the relationship between convergence time and the structure of the underlying digraph. We illustrate our theoretical findings via numerical simulations towards the end of the paper.
We study the problem of robust global synchronization of pulse-coupled oscillators (PCOs) over directed graphs. It is known that when the digraphs are strongly connected, global synchronization can be achieved by using a class of deterministic set-valued reset controllers. However, for large-scale networks, these algorithms are not scalable because some of their tuning parameters have upper bounds of the order of O(1/N), where N is the number of agents. This paper resolves this scalability issue by presenting several new results in the context of global synchronization of PCOs with more general network topologies using deterministic and stochastic hybrid dynamical systems. First, we establish that similar deterministic resetting algorithms can achieve robust, global, and fixed-time synchronization in any rooted acyclic digraph. Moreover, in this case we show that the synchronization dynamics are now scalable as the tuning parameters of the algorithm are network independent, i.e., of order O(1). However, the algorithms cannot be further extended to all rooted digraphs. We establish this new impossibility result by introducing a counterexample with a particular rooted digraph for which global synchronization cannot be achieved, irrespective of the tuning of the reset rule. Nevertheless, we show that if the resetting algorithms are modified by accommodating an Erdos-Renyi type random graph model, then the resulting stochastic resetting dynamics will guarantee global synchronization almost surely for all rooted digraphs and, moreover, the tunable parameters of the dynamics are network independent. Stability and robustness properties of the resetting algorithms are studied using the tools from set-valued hybrid dynamical systems. Numerical simulations are provided at the end of the paper for demonstration of the main results.
Today the gold standard for in vivo imaging through scattering tissue is the point-scanning two-photon microscope (PSTPM). Especially in neuroscience, PSTPM is widely used for deep-tissue imaging in the brain. However, due to sequential scanning, PSTPM is slow. Temporal focusing microscopy (TFM), on the other hand, focuses femtosecond pulsed laser light temporally, while keeping wide-field illumination, and is consequently much faster. However, due to the use of a camera detector, TFM suffers from the scattering of emission photons. As a result, TFM produces images of poor spatial resolution and signal-to-noise ratio (SNR), burying fluorescent signals from small structures such as dendritic spines. In this work, we present a data-driven deep learning approach to improve resolution and SNR of TFM images. Using a 3D convolutional neural network (CNN) we build a map from TFM to PSTPM modalities, to enable fast TFM imaging while maintaining high-resolution through scattering media. We demonstrate this approach for in vivo imaging of dendritic spines on pyramidal neurons in the mouse visual cortex. We show that our trained network rapidly outputs high-resolution images that recover biologically relevant features previously buried in the scattered fluorescence in the TFM images. In vivo imaging that combines TFM and the proposed 3D convolution neural network is one to two orders of magnitude faster than PSTPM but retains the high resolution and SNR necessary to analyze small fluorescent structures. The proposed 3D convolution deep network could also be potentially beneficial for improving the performance of many speed-demanding deep-tissue imaging applications such as in vivo voltage imaging.