arXiv subjects

Chuanhou Gao

Publications and source records attributed to Chuanhou Gao.

At least 19 recordsLinked to original sources

arXiv2026

Input-to-state stability of chemical reaction networks with application to molecular computation

Input-to-state stability (ISS) provides a useful tool for analyzing the robustness of time-varying chemical reaction networks (CRNs). This paper investigates the ISS property for CRNs in two cases: one is for weakly reversible CRNs with nonzero deficiency and multiple linkage classes, which is beyond the limit of existing results requesting a weakly reversible CRN to be zero-deficiency and single-linkage-class; the other is for non-weakly reversible CRNs by leveraging the notion of linear conjugacy. These results, on the one hand enrich the studies of the ISS property of broader classes of CRNs, on the other hand serve for designing CRN-based molecular computing systems. The latter application suggests the ISS theory can justify the parallel mechanism of biomolecular computations. We use some CRNs of practical relevance to demonstrate our results, including the p53 signaling and dimerization network, the p21-activated kinase 1 network, etc.

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arXiv2026

On the Convergence Rate Lower Bound of Biochemical Computational Modules

Biochemical reaction networks have become a central theoretical framework for implementing molecular computation. A key challenge is finite time computational accuracy, as computation outputs are encoded in limiting steady states (LSSs) of species concentrations while practical implementations operate for only finite time. This work proposes a concise characterization of convergence rate for biochemical computational modules with multiple output species, and rigorously establishes it as being bounded by the eigenvalue with largest (least negative) real part of the Jacobian matrix. Two numerical examples illustrate how the theoretical lower bound shapes the convergence rate range and reveals its dependence on reaction rate constants. This formulation enables systematic evaluation of biochemical computation speed and provides a practical design measure for constructing high-accuracy and error-controlled biochemical computational modules.

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arXiv2025

Structure-conditioned input-to-state stability for layer-by-layer molecular computations in parallel chemical reaction networks

Molecular computation in chemical reaction networks (CRNs) now constitutes a foundational framework for designing programmable biological systems. However, prevailing design methodologies primarily treat parallelism of chemical reactions as a liability, consequently motivating researchers to redirect research focus toward leveraging parallelism to implement layer-by-layer computations of composite functions in coupled mass-action systems (MASs). MASs exhibiting this property are termed composable. Present composability verification for MASs mainly depends on input-to-state stability (ISS) conditions, with structural characteristics of networks remaining underexplored. This paper investigates the structural conditions under which two MASs are composable. By leveraging ISS-Lyapunov functions, we identify a class of CRN architectures, whose reduced systems have zero deficiency, that guarantee composability with other networks. We also extend our conclusions to encompass some CRN architectures possessing nonzero deficiency. Some examples are presented to demonstrate the validity of our theoretical results. Finally, we employ our methods to devise an algorithm for constructing MASs capable of executing specified molecular computations.

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arXiv2025

Structure and input-to-state stability for composable computations in chemical reaction networks

In the field of molecular computation based on chemical reaction networks (CRNs), leveraging parallelism to enable coupled mass-action systems (MASs) to retain predefined computational functionality has been a research focus. MASs exhibiting this property are termed composable. This paper investigates the structural conditions under which two MASs are composable. By leveraging input-to-state stability (ISS) property, we identify a specific class of CRN architectures that guarantee composability with other networks. A concrete example demonstrates the validity of this conclusion and illustrates the application of composability in computing composite functions.

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arXiv2025

Sparse Convex Quantile Regression: A Generalized Benders Decomposition Approach

We develop a scalable algorithmic framework for sparse convex quantile regression (SCQR), addressing key computational challenges in the literature. Enhancing the classical CQR model, we introduce L2-norm regularization and an epsilon-insensitive zone to improve generalization and mitigate overfitting - both theoretically justified and empirically validated. Based on this extension, we improve the SCQR model and propose the first Generalized Benders Decomposition (GBD) algorithm tailored to this context, further strengthened by a novel local search-based Benders matheuristic. Extensive simulations and a real-world application to Sustainable Development Goals benchmarking demonstrate the accuracy, scalability, and practical value of our approach.

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arXiv2025

LILI clustering algorithm: Limit Inferior Leaf Interval Integrated into Causal Forest for Causal Interference

Causal forest methods are powerful tools in causal inference. Similar to traditional random forest in machine learning, causal forest independently considers each causal tree. However, this independence consideration increases the likelihood that classification errors in one tree are repeated in others, potentially leading to significant bias in causal e ect estimation. In this paper, we propose a novel approach that establishes connections between causal trees through the Limit Inferior Leaf Interval (LILI) clustering algorithm. LILIs are constructed based on the leaves of all causal trees, emphasizing the similarity of dataset confounders. When two instances with di erent treatments are grouped into the same leaf across a su cient number of causal trees, they are treated as counterfactual outcomes of each other. Through this clustering mechanism, LILI clustering reduces bias present in traditional causal tree methods and enhances the prediction accuracy for the average treatment e ect (ATE). By integrating LILIs into a causal forest, we develop an e cient causal inference method. Moreover, we explore several key properties of LILI by relating it to the concepts of limit inferior and limit superior in the set theory. Theoretical analysis rigorously proves the convergence of the estimated ATE using LILI clustering. Empirically, extensive comparative experiments demonstrate the superior performance of LILI clustering.

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arXiv2025

Input-to-state stability-based chemical reaction networks composition for molecular computations

Molecular computation based on chemical reaction networks (CRNs) has emerged as a promising paradigm for designing programmable biochemical systems. However, the implementation of complex computations still requires excessively large and intricate network structures, largely due to the limited understanding of composability, that is, how multiple subsystems can be coupled while preserving computational functionality. Existing composability frameworks primarily focus on rate-independent CRNs, whose computational capabilities are severely restricted. This article aims to establish a systematic framework for composable CRNs governed by mass-action kinetics, a common type of rate-dependent CRNs. Drawing upon the concepts of composable rate-independent CRNs, we introduce the notions of mass-action chemical reaction computers (msCRCs), dynamic computation and dynamic composability to establish a rigorous mathematical framework for composing two or more msCRCs to achieve layer-by-layer computation of composite functions. Further, we derive several sufficient conditions based on the notions of input-to-state stability (ISS) to characterize msCRCs that can be composed to implement desired molecular computations, thereby providing theoretical support for this framework. Some examples are presented to illustrate the efficiency of our method. Finally, comparative results demonstrate that the proposed method exhibits notable advantages in both computational ability and accuracy over the state-of-the-art methods.

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arXiv2025

Disentangled Graph Autoencoder for Treatment Effect Estimation

Treatment effect estimation from observational data has attracted significant attention across various research fields. However, many widely used methods rely on the unconfoundedness assumption, which is often unrealistic due to the inability to observe all confounders, thereby overlooking the influence of latent confounders. To address this limitation, recent approaches have utilized auxiliary network information to infer latent confounders, relaxing this assumption. However, these methods often treat observed variables and networks as proxies only for latent confounders, which can result in inaccuracies when certain variables influence treatment without affecting outcomes, or vice versa. This conflation of distinct latent factors undermines the precision of treatment effect estimation. To overcome this challenge, we propose a novel disentangled variational graph autoencoder for treatment effect estimation on networked observational data. Our graph encoder disentangles latent factors into instrumental, confounding, adjustment, and noisy factors, while enforcing factor independence using the Hilbert-Schmidt Independence Criterion. Extensive experiments on multiple networked datasets demonstrate that our method outperforms state-of-the-art approaches.

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arXiv2024

Causal Flow-based Variational Auto-Encoder for Disentangled Causal Representation Learning

Disentangled representation learning aims to learn low-dimensional representations where each dimension corresponds to an underlying generative factor. While the Variational Auto-Encoder (VAE) is widely used for this purpose, most existing methods assume independence among factors, a simplification that does not hold in many real-world scenarios where factors are often interdependent and exhibit causal relationships. To overcome this limitation, we propose the Disentangled Causal Variational Auto-Encoder (DCVAE), a novel supervised VAE framework that integrates causal flows into the representation learning process, enabling the learning of more meaningful and interpretable disentangled representations. We evaluate DCVAE on both synthetic and real-world datasets, demonstrating its superior ability in causal disentanglement and intervention experiments. Furthermore, DCVAE outperforms state-of-the-art methods in various downstream tasks, highlighting its potential for learning true causal structures among factors.

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arXiv2024

Learning Network Representations with Disentangled Graph Auto-Encoder

The (variational) graph auto-encoder is widely used to learn representations for graph-structured data. However, the formation of real-world graphs is a complicated and heterogeneous process influenced by latent factors. Existing encoders are fundamentally holistic, neglecting the entanglement of latent factors. This reduces the effectiveness of graph analysis tasks, while also making it more difficult to explain the learned representations. As a result, learning disentangled graph representations with the (variational) graph auto-encoder poses significant challenges and remains largely unexplored in the current research. In this paper, we introduce the Disentangled Graph Auto-Encoder (DGA) and the Disentangled Variational Graph Auto-Encoder (DVGA) to learn disentangled representations. Specifically, we first design a disentangled graph convolutional network with multi-channel message-passing layers to serve as the encoder. This allows each channel to aggregate information about each latent factor. The disentangled variational graph auto-encoder's expressive capability is then enhanced by applying a component-wise flow to each channel. In addition, we construct a factor-wise decoder that takes into account the characteristics of disentangled representations. We improve the independence of representations by imposing independence constraints on the mapping channels for distinct latent factors. Empirical experiments on both synthetic and real-world datasets demonstrate the superiority of our proposed method compared to several state-of-the-art baselines.

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arXiv2024

Stability Analysis of Biochemical Reaction Networks Linearly Conjugated to complex balanced Systems with Time Delays Added

Linear conjugacy offers a new perspective to broaden the scope of stable biochemical reaction networks to the systems linearly conjugated to the well-established complex balanced mass action systems ($\ell$cCBMASs). This paper addresses the challenge posed by time delay, which can disrupt the linear conjugacy relationship and complicate stability analysis for delayed versions of $\ell$cCBMASs (D$\ell$cCBMAS). Firstly, we develop Lyapunov functionals tailored to some D$\ell$cCBMASs by using the persisted parameter relationships under time delays. Subsequently, we redivide the phase space as several invariant sets of trajectories and further investigate the existence and uniqueness of equilibriums in each newly defined invariant set. This enables us to determine the local asymptotic stability of some D$\ell$cCBMASs within an updated framework. Furthermore, illustrative examples are provided to demonstrate the practical implications of our approach.

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arXiv2024

Learn to formulate: A surrogate model framework for generalized assignment problem with routing constraints

The generalized assignment problem with routing constraints, e.g. the vehicle routing problem, has essential practical relevance. This paper focuses on addressing the complexities of the problem by learning a surrogate model with reduced variables and reconstructed constraints. A surrogate model framework is presented with a class of surrogate models and a learning method to acquire parameters. The paper further provides theoretical results regarding the representational power and statistical properties to explore the effectiveness of this framework. Numerical experiments based on two practical problem classes demonstrate the accuracy and efficiency of the framework. The resulting surrogate models perform comparably to or surpass the state-of-the-art heuristics on average. Our findings provide empirical evidence for the effectiveness of utilizing size-reduced and reconstructed surrogate models in producing high-quality solutions.

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arXiv2024

Some dynamical properties of delayed weakly reversible mass-action systems

This paper focuses on the dynamical properties of delayed complex balanced systems. We first study the relationship between the stoichiometric compatibility classes of delayed and non-delayed systems. Using this relation we give another way to derive the existence of positive equilibrium in each stoichiometric compatibility class for delayed complex balanced systems. And if time delays are constant, the result can be generalized to weakly reversible networks. Also, by utilizing the Lyapunov-Krasovskii functional, we can obtain a long-time dynamical property about $ω$-limit set of the complex balanced system with constant time delays. An example is also provided to support our results.

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arXiv2024

Automatic Implementation of Neural Networks through Reaction Networks--Part II: Error Analysis

This paired article aims to develop an automated and programmable biochemical fully connected neural network (BFCNN) with solid theoretical support. In Part I, a concrete design for BFCNN is presented, along with the validation of the effectiveness and exponential convergence of computational modules. In this article, we establish the framework for specifying the realization errors by monitoring the errors generated from approaching equilibrium points in individual modules, as well as their vertical propagation from upstream modules and horizontal accumulation from previous iterations. Ultimately, we derive the general error upper bound formula for any iteration and illustrate its exponential convergence order with respect to the phase length of the utilized chemical oscillator. The numerical experiments, based on the classification examples, reveal the tendency of total errors related to both the phase length and iteration number.

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arXiv2024

Controlling the occurrence sequence of reaction modules through biochemical relaxation oscillators

Embedding sequential computations in biochemical environments is challenging because the computations are carried out by chemical reactions, which are inherently disordered. In this paper we apply modular design to specific calculations through chemical reactions and provide a design scheme of biochemical oscillator models in order to generate periodical species for the order regulation of these reaction modules. We take the case of arbitrary multi-module regulation into consideration, analyze the main errors in the regulation process under \textit{mass-action kinetics} and demonstrate our design scheme under existing synthetic biochemical oscillator models.

q-bio.MN↗

arXiv2023

ADPBA: Efficiently generating Lagrangian cuts for two-stage stochastic integer programs

The use of Lagrangian cuts proves effective in enhancing the lower bound of the master problem within the execution of benders-type algorithms, particularly in the context of two-stage stochastic programs. However, even the process of generating a single Lagrangian cut is notably time-intensive. In light of this challenge, we present a novel framework that integrates Lagrangian cut generation with an adaptive partition-based approach, thereby mitigating this time-related drawback to a considerable extent. Furthermore, we also discuss the dominance relationship between the generated partition-based Lagrangian cut and the Lagrangian cut for the original problem. To provide empirical evidence of our approach's efficacy, we undertake an extensive computational study encompassing instances involving even up to a thousand scenarios. The results of this study conclusively demonstrate the superiority and efficiency of the proposed methodology.

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arXiv2023

Automatic Implementation of Neural Networks through Reaction Networks -- Part I: Circuit Design and Convergence Analysis

Information processing relying on biochemical interactions in the cellular environment is essential for biological organisms. The implementation of molecular computational systems holds significant interest and potential in the fields of synthetic biology and molecular computation. This two-part article aims to introduce a programmable biochemical reaction network (BCRN) system endowed with mass action kinetics that realizes the fully connected neural network (FCNN) and has the potential to act automatically in vivo. In part I, the feedforward propagation computation, the backpropagation component, and all bridging processes of FCNN are ingeniously designed as specific BCRN modules based on their dynamics. This approach addresses a design gap in the biochemical assignment module and judgment termination module and provides a novel precise and robust realization of bi-molecular reactions for the learning process. Through equilibrium approaching, we demonstrate that the designed BCRN system achieves FCNN functionality with exponential convergence to target computational results, thereby enhancing the theoretical support for such work. Finally, the performance of this construction is further evaluated on two typical logic classification problems.

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arXiv2023

Causal Structure Learning by Using Intersection of Markov Blankets

In this paper, we introduce a novel causal structure learning algorithm called Endogenous and Exogenous Markov Blankets Intersection (EEMBI), which combines the properties of Bayesian networks and Structural Causal Models (SCM). Furthermore, we propose an extended version of EEMBI, namely EEMBI-PC, which integrates the last step of the PC algorithm into EEMBI.

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