arXiv subjects

Haoyu Yin

Publications and source records attributed to Haoyu Yin.

8 recordsLinked to original sources

arXiv2026

On Coexistence of Conservative Replicator Dynamics with Four Strategies

In this paper, we study four-strategy conservative replicator dynamics induced by constant payoff matrices. We establish necessary and sufficient conditions for coexistence to occur by associating the payoff matrix with its digraph, revealing exactly five distinct digraph classes governing the global behavior. We further show that, whenever the dynamics is coexistent, every non-equilibrium trajectory in the relative interior of the simplex is a Lyapunov-stable periodic orbit. Together with the classification of the boundary phase portraits, these results provide a complete characterization of the global dynamics in the four-strategy case with coexistence.

math.DS↗

arXiv2025

Switched Linear Ensemble Systems and Structural Controllability

This paper introduces and solves a structural controllability problem for ensembles of switched linear systems. All individual systems in the ensemble are sparse and governed by the same sparsity pattern, and undergo switching among subsystems by following the same switching sequence. The controllability of an ensemble system describes the ability to use a common control input to simultaneously steer every individual system. A sparsity pattern is called structurally controllable for pair $(k,q)$ if it admits a controllable ensemble of $q$ individual systems with at most $k$ subsystems. We derive a necessary and sufficient condition for a sparsity pattern to be structurally controllable for a given $(k,q)$, and characterize when a sparsity pattern admits a finite $k$ that guarantees structural controllability for $(k,q)$ for arbitrary $q$. Compared with the linear time-invariant ensemble case, this second condition is strictly weaker. We further show that these conditions have natural connections with maximum flow, and hence can be checked by polynomial algorithms. Specifically, the time complexity of deciding structural controllability is $O(n^3)$ and the complexity of computing the smallest number of subsystems needed is $O(n^3 \log n)$, with $n$ the dimension of each individual system.

math.OC↗

arXiv2025

On Zero-sum Game Representation for Replicator Dynamics

Replicator dynamics have been widely used in evolutionary game theory to model how strategy frequencies evolve over time in large populations. The so-called payoff matrix encodes the pairwise fitness that each strategy obtains when interacting with every other strategy, and it solely determines the replicator dynamics. If the payoff matrix is unknown, we show in this paper that it cannot be inferred from observed strategy frequencies alone -- distinct payoff matrices can induce the same replicator dynamics. We thus look for a canonical representative of the payoff matrix in the equivalence class. The main result of the paper is to show that for every polynomial replicator dynamics (i.e., the vector field is a polynomial), there always exists a skew-symmetric, polynomial payoff matrix that can induce the given dynamics.

math.DS↗

arXiv2025

Admission Control for A Single Server Waiting Time Process in Heavy Traffic

We address a single server queue control problem (QCP) in heavy traffic originating from Lee and Weerasinghe (2011). The state process represents the offered waiting time, the customer arrival has a state-dependent intensity, and the customers' service and patience times are i.i.d with general distributions. We introduce an infinite-horizon discounted cost functional consisting of a control cost generated from the use of control and a penalty for idleness cost. Our primary goal is to tackle the QCP, taking into account a non-trivial control cost and a non-increasing cost function resulting from the control mechanisms in the waiting time. Under mild assumptions, the heavy traffic limit of the QCP yields a stochastic control problem described by a diffusion process, which we call a diffusion control problem (DCP). We find the optimal control of the associated DCP by incorporating the Legendre-Fenchel transform and a formal Hamilton-Jacobi-Bellman (HJB) equation. Then, we ``translate'' this optimal strategy to the QCP, of which we obtain an asymptotically optimal policy. Apart from theoretical results, we also examine the REINFORCE algorithm, a Reinforcement learning (RL) approach, for solving stochastic controls motivated by recent literature. We highlight the advantages and limitations of simulation from theoretical results and data-driven algorithms.

math.OC↗

arXiv2025

AutoMat: Enabling Automated Crystal Structure Reconstruction from Microscopy via Agentic Tool Use

Reconstructing atomistic crystal structures from a single noisy STEM projection is an ill-posed inverse problem: multiple lattices can explain similar contrast, and purely feed-forward models cannot verify physical validity. We present AutoMat, a failure-aware agentic controller that performs inference-time hypothesis search with closed-loop verification to convert Scanning Transmission Electron Microscopy (STEM) images into simulation-ready crystal structures and downstream properties. AutoMat composes perception and physics modules---pattern-adaptive denoising, physics-guided template retrieval as a state-dependent auxiliary branch, symmetry-constrained atomic reconstruction, and MLIP-based relaxation/validation---and triggers rollback-and-retry when verification fails. For systematic evaluation, we introduce STEM2Mat-Bench, a benchmark dataset containing 450+ annotated samples. Performance is assessed using lattice root-mean-square deviation (RMSD), formation energy mean absolute error (MAE), and structure matching accuracy. Results demonstrate that AutoMat outperforms existing approaches including SOTA models, specialized domain tools, and closed-source multimodal large models. This work establishes a direct pathway from microscopic characterization to atomic-scale modeling, addressing a fundamental challenge in materials science.

cs.CV↗

arXiv2024

Integrating Chemistry Knowledge in Large Language Models via Prompt Engineering

This paper presents a study on the integration of domain-specific knowledge in prompt engineering to enhance the performance of large language models (LLMs) in scientific domains. A benchmark dataset is curated to encapsulate the intricate physical-chemical properties of small molecules, their drugability for pharmacology, alongside the functional attributes of enzymes and crystal materials, underscoring the relevance and applicability across biological and chemical domains.The proposed domain-knowledge embedded prompt engineering method outperforms traditional prompt engineering strategies on various metrics, including capability, accuracy, F1 score, and hallucination drop. The effectiveness of the method is demonstrated through case studies on complex materials including the MacMillan catalyst, paclitaxel, and lithium cobalt oxide. The results suggest that domain-knowledge prompts can guide LLMs to generate more accurate and relevant responses, highlighting the potential of LLMs as powerful tools for scientific discovery and innovation when equipped with domain-specific prompts. The study also discusses limitations and future directions for domain-specific prompt engineering development.

cs.CL↗

arXiv2020

Decentralized Optimization over Tree Graphs

This paper presents a decentralized algorithm for non-convex optimization over tree-structured networks. We assume that each node of this network can solve small-scale optimization problems and communicate approximate value functions with its neighbors based on a novel multi-sweep communication protocol. In contrast to existing parallelizable optimization algorithms for non-convex optimization the nodes of the network are neither synchronized nor assign any central entity. None of the nodes needs to know the whole topology of the network, but all nodes know that the network is tree-structured. We discuss conditions under which locally quadratic convergence rates can be achieved. The method is illustrated by running the decentralized asynchronous multi-sweep protocol on a radial AC power network case study.

math.OC↗

arXiv2019

Centralized Coded Caching with User Cooperation

In this paper, we consider the coded-caching broadcast network with user cooperation, where a server connects with multiple users and the users can cooperate with each other through a cooperation network. We propose a centralized coded caching scheme based on a new deterministic placement strategy and a parallel delivery strategy. It is shown that the new scheme optimally allocate the communication loads on the server and users, obtaining cooperation gain and parallel gain that greatly reduces the transmission delay. Furthermore, we show that the number of users who parallelly send information should decrease when the users' caching size increases. In other words, letting more users parallelly send information could be harmful. Finally, we derive a constant multiplicative gap between the lower bound and upper bound on the transmission delay, which proves that our scheme is order optimal.

cs.IT↗