arXiv subjects

Chao Min

Publications and source records attributed to Chao Min.

At least 19 recordsLinked to original sources

arXiv2026

Generalized Freud weight, discrete Painlev\'{e} I hierarchy and full asymptotics of Hankel determinants

In this paper, we investigate the monic orthogonal polynomials $P_{n}(x;T_{m};\lambda)$ and the Hankel determinants $D_{n}(T_{m}; \lambda)$ associated with the generalized Freud weight \[w(x;T_{m};\lambda) = |x|^{2\lambda+1}\exp\biggl(-\sum_{k=1}^m t_k x^{2k}\biggr),\quad m \in \mathbb{Z}^+,\; t_{k} \in \mathbb{R} , x\in\mathbb{R}\setminus\{0\},\] where $T_{m}=\{t_{1},t_{2},\cdots, t_{m}\}$, $t_{m}>0$ and $\lambda>-1$.By employing ladder operators and compatibility conditions, we find that all members of the discrete Painlev\'{e} I hierarchy have a unified structure and the recurrence coefficient $\beta_n$ of $P_{n}(x;T_{m};\lambda)$ satisfies the $m$-th member of the discrete Painlev\'{e} I hierarchy. Besides, we derive the second-order differential equation satisfied by $P_{n}(x;T_{m};\lambda)$, the partial derivatives of the recurrence coefficients $\beta_n$ with respect to parameters $t_1, t_2, \dots, t_{m-1}$ and the corresponding differential identities for $D_{n}(T_{m}; \lambda)$. Based on the discrete Painlev\'{e} I hierarchy and the above differential identities, we obtain new partial differential equations satisfied by $\ln\beta_n$ and $\ln D_{n}(T_{m}; \lambda)$.Using the discrete Painlev\'{e} I hierarchy and the asymptotic theory of linear difference equations, we derive the full asymptotic expansions of the recurrence coefficient $\beta_n$, the nontrivial leading coefficient $\mathrm{p}(n; T_m; \lambda)$, and the Hankel determinant $D_n(T_m; \lambda)$ as $n\to\infty$, for general $T_m$ and $\lambda>-1$. Notably, while the logarithmic term $\ln n$ appears in the leading-order contributions, it is absent from the remainder terms in these expansions.We illustrate our results under the specific decic Freud weight $w(x;t_1,t_2;\lambda)=|x|^{2\lambda+1} \exp\bigl(-x^{10}-t_2x^4-t_1x^2\bigr)$.

math.CA↗

arXiv2026

TRUST-TAEA: A trustworthiness-guided two-archive evolutionary algorithm with variable-grouping sparse search for large-scale multi-objective optimization

Large-scale multi-objective optimization problems (LSMOPs) remain challenging due to the high-dimensional decision spaces, complex variable interactions, and limited function evaluation budgets, which make it difficult to balance the convergence, diversity, and stability. Existing two-archive evolutionary algorithms can alleviate the conflict between convergence and diversity, but they often underuse archive reliability and problem-structure information, leading to inefficient search, incomplete front coverage, and late-stage archive drift. To address these issues, this paper proposes TRUST-TAEA, a trustworthiness-guided two-archive evolutionary algorithm. Archive trustworthiness is defined by integrating evolutionary progress with convergence-archive maturity, and is used to coordinate variable-grouping sparse search, anchor-probing compensatory search, and archive stabilization. TRUST-TAEA is evaluated on the LSMOP benchmark suite with 500--5000 decision variables and 2, 3-objectives. Experimental results show that TRUST-TAEA achieves superior and highly competitive performance in terms of convergence, diversity, and stability. A three-objective day-ahead scheduling case of a grid-connected microgrid further demonstrates its practical applicability, where TRUST-TAEA obtains the best IGD$^+$ value and generates a feasible dispatch strategy balancing cost, emissions, and grid-power fluctuation.

math.OC↗

arXiv2026

The multi-objective portfolio model for oil and gas exploration drilling projects selection and its operator-enhanced NSGA-II based solution

Drilling investment is pivotal to operational planning in oil and gas (O\&G) exploration. Conventional deployment relies heavily on fragmented expert assessments of geological and economic factors, with limited integration ability of information. As the tool of portfolio show strong potential for mitigating uncertainty and selecting superior drilling plans, this study develops a multi-objective mean-variance portfolio model that accounts for geological-parameter uncertainty, enabling an effective risk-return trade-off and optimal selection. First, the probabilistic distribution of geological-parameters for prospect-list projects is obtained through expert-elicited priors. And considering the selection of the drilling projects as a portfolio, an optimization model is formulated jointly to describe the return and risk of short-term plan, under different constraints. Second, an improved OE-NSGA-II algorithm is proposed specifically for this model, in which (1) a directional crossover operator is designed to embed improving directions in objective space-derived from dominance and objective differences-into recombination, and (2) a structure-aware mutation operator is designed to prioritize high-utility bit flips via probabilistic sampling with feasibility repair, thus improving the search ability for superior Pareto solutions. Finally, using the case of 2023 exploration drilling deployment for verification, and then apply the validated method to the 2024 deployment to support decision-making. The results indicate that the proposed approach offers a reusable solution for drilling portfolio optimization in O\&G exploration.

math.OC↗

arXiv2025

Orthogonal polynomials for the singularly perturbed Laguerre weight, Hankel determinants and asymptotics

Based on the work of Chen and Its [{\em J. Approx. Theory} {\bf 162} ({2010}) {270--297}], we further study orthogonal polynomials with respect to the singularly perturbed Laguerre weight $w(x;t,\alpha) = {x^\alpha}{\mathrm e^{- x-\frac{t}{x}}}, \; x\in\mathbb{R}^{+},\;\alpha > -1,\; t\geq 0$. By using the ladder operators and associated compatibility conditions for orthogonal polynomials with general Laguerre-type weights, we derive the second-order differential equation satisfied by the orthogonal polynomials, a system of difference equations and a system of differential-difference equations for the recurrence coefficients. We also investigate the properties of the zeros of the orthogonal polynomials. Using Dyson's Coulomb fluid approach together with the discrete system, we obtain the large $n$ asymptotic expansions of the recurrence coefficients, the sub-leading coefficient of the monic orthogonal polynomials, the Hankel determinant and the normalized constant for fixed $t>0$. It is found that all the asymptotic expansions are singular at $t=0$. We also study the long-time ($t\rightarrow+\infty$) asymptotics of these quantities explicitly for fixed $n\in\mathbb{N}$ from the Toda-type system.

math.CA↗

arXiv2025

Asymptotics of the Hankel determinant and orthogonal polynomials arising from the information theory of MIMO systems

We consider the Hankel determinant and orthogonal polynomials with respect to the deformed Laguerre weight $w(x; t) = {x^\alpha }{\mathrm e^{ - x}}{(x + t)^\lambda },\; x\in \mathbb{R}^{+} $ with parameters $\alpha > -1,\; t > 0$ and $\lambda \in \mathbb{R}$. This problem originates from the information theory of single-user multiple-input multiple-output (MIMO) systems studied by Chen and McKay [{\em IEEE Trans. Inf. Theory} {\bf 58} ({2012}) {4594--4634}]. By using the ladder operators for orthogonal polynomials with general Laguerre-type weights, we obtain a system of difference equations and a system of differential-difference equations for the recurrence coefficients $\alpha_n(t)$ and $\beta_n(t)$. We also show that the orthogonal polynomials satisfy a second-order ordinary differential equation. By using Dyson's Coulomb fluid approach, we obtain the large $n$ asymptotic expansions of the recurrence coefficients $\alpha_n(t)$ and $\beta_n(t)$, the sub-leading coefficient $\mathrm p(n, t)$ of the monic orthogonal polynomials, the Hankel determinant $D_n(t)$ and the normalized constant $h_n(t)$ for fixed $t\in\mathbb{R}^{+}$. We also discuss the long-time asymptotics of these quantities as $t\rightarrow\infty$ for fixed $n\in\mathbb{N}$. The large $n$ and large $t$ asymptotics of the above quantities are very important for the study of the asymptotics of the mutual information distribution and two fundamental quantities (the outage capacity and the error probability) for single-user MIMO systems.

math-ph↗

arXiv2024

The discrete Painlev\'{e} XXXIV hierarchy arising from the gap probability distributions of Freud random matrix ensembles

We consider the symmetric gap probability distributions of certain Freud unitary ensembles. This problem is related to the Hankel determinants generated by the Freud weights supported on the complement of a symmetric interval. By using Chen and Ismail's ladder operator approach, we obtain the difference equations satisfied by the recurrence coefficients for the orthogonal polynomials with the discontinuous Freud weights. We find that these equations, with a minor change of variables, are the discrete Painlev\'{e} XXXIV hierarchy proposed by Cresswell and Joshi [{\em J. Phys. A: Math. Gen.} {\bf 32} ({1999}) {655--669}]. This is the first time that the discrete Painlev\'{e} XXXIV hierarchy appears in the study of Random Matrix Theory. We also derive the differential-difference equations for the recurrence coefficients and show the relationship between the logarithmic derivative of the gap probabilities, the nontrivial leading coefficients of the monic orthogonal polynomials and the recurrence coefficients.

nlin.SI↗

arXiv2024

Hankel determinant and orthogonal polynomials arising from the matrix model in 2D quantum gravity

We study the Hankel determinant and orthogonal polynomials with respect to the two-parameter weight function $$ w(x)=w(x;t_1, t_2):=\exp(-x^6-t_2 x^4-t_1 x^2),\qquad x\in\mathbb{R}, $$ with $t_1,\; t_2 \in \mathbb{R}$. This problem arises from the matrix model in 2D quantum gravity investigated by Fokas, Its and Kitaev [Commun. Math. Phys. \textbf{142} (1991) 313--344]. By making use of the ladder operator approach, we find that the recurrence coefficient $\beta_{n}(t_1,t_2)$ for the monic orthogonal polynomials satisfies a nonlinear fourth-order difference equation, which is within the discrete Painlev\'{e} I hierarchy. We show that the orthogonal polynomials satisfy a second-order linear differential equation whose coefficients are all expressed in terms of $\beta_{n}(t_1,t_2)$. The relations between the logarithmic partial derivative of the Hankel determinant, the nontrivial leading coefficient of the monic orthogonal polynomials, and the recurrence coefficient are established. By using Dyson's Coulomb fluid approach, we obtain the large $n$ asymptotic expansions of the recurrence coefficient $\beta_{n}(t_1,t_2)$, the nontrivial leading coefficient $\mathrm{p}(n,t_1,t_2)$, the normalized constant $h_n(t_1,t_2)$ and the Hankel determinant $D_{n}(t_1,t_2)$.

math-ph↗

arXiv2024

Generalized Airy polynomials, Hankel determinants and asymptotics

We further study the orthogonal polynomials with respect to the generalized Airy weight based on the work of Clarkson and Jordaan [{\em J. Phys. A: Math. Theor.} {\bf 54} ({2021}) {185202}]. We prove the ladder operator equations and associated compatibility conditions for orthogonal polynomials with respect to a general Laguerre-type weight of the form $w(x)=x^\lambda w_0(x),\;\lambda>-1, x\in\mathbb{R}^+$. By applying them to the generalized Airy polynomials, we are able to derive a discrete system for the recurrence coefficients. Combining with the Toda evolution, we establish the relation between the recurrence coefficients, the sub-leading coefficient of the monic generalized Airy polynomials and the associated Hankel determinant. Using Dyson's Coulomb fluid approach and with the aid of the discrete system for the recurrence coefficients, we obtain the large $n$ asymptotic expansions for the recurrence coefficients and the sub-leading coefficient of the monic generalized Airy polynomials. The large $n$ asymptotic expansion (including the constant term) of the Hankel determinant has been derived by using a recent result in the literature. The long-time asymptotics of these quantities have also been discussed explicitly.

math-ph↗

arXiv2024

A multi-source data power load forecasting method using attention mechanism-based parallel cnn-gru

Accurate power load forecasting is crucial for improving energy efficiency and ensuring power supply quality. Considering the power load forecasting problem involves not only dynamic factors like historical load variations but also static factors such as climate conditions that remain constant over specific periods. From the model-agnostic perspective, this paper proposes a parallel structure network to extract important information from both dynamic and static data. Firstly, based on complexity learning theory, it is demonstrated that models integrated through parallel structures exhibit superior generalization abilities compared to individual base learners. Additionally, the higher the independence between base learners, the stronger the generalization ability of the parallel structure model. This suggests that the structure of machine learning models inherently contains significant information. Building on this theoretical foundation, a parallel convolutional neural network (CNN)-gate recurrent unit (GRU) attention model (PCGA) is employed to address the power load forecasting issue, aiming to effectively integrate the influences of dynamic and static features. The CNN module is responsible for capturing spatial characteristics from static data, while the GRU module captures long-term dependencies in dynamic time series data. The attention layer is designed to focus on key information from the spatial-temporal features extracted by the parallel CNN-GRU. To substantiate the advantages of the parallel structure model in extracting and integrating multi-source information, a series of experiments are conducted.

cs.LG↗

arXiv2024

Domain Adaptation for Industrial Time-series Forecasting via Counterfactual Inference

Industrial time-series, as a structural data responds to production process information, can be utilized to perform data-driven decision-making for effective monitoring of industrial production process. However, there are some challenges for time-series forecasting in industry, e.g., predicting few-shot caused by data shortage, and decision-confusing caused by unknown treatment policy. To cope with the problems, we propose a novel causal domain adaptation framework, Causal Domain Adaptation (CDA) forecaster to improve the performance on the interested domain with limited data (target). Firstly, we analyze the causality existing along with treatments, and thus ensure the shared causality over time. Subsequently, we propose an answer-based attention mechanism to achieve domain-invariant representation by the shared causality in both domains. Then, a novel domain-adaptation is built to model treatments and outcomes jointly training on source and target domain. The main insights are that our designed answer-based attention mechanism allows the target domain to leverage the existed causality in source time-series even with different treatments, and our forecaster can predict the counterfactual outcome of industrial time-series, meaning a guidance in production process. Compared with commonly baselines, our method on real-world and synthetic oilfield datasets demonstrates the effectiveness in across-domain prediction and the practicality in guiding production process

cs.LG↗

arXiv2024

Orthogonal Polynomials with a Singularly Perturbed Airy Weight

We study the monic orthogonal polynomials with respect to a singularly perturbed Airy weight. By using Chen and Ismail's ladder operator approach, we derive a discrete system satisfied by the recurrence coefficients for the orthogonal polynomials. We find that the orthogonal polynomials satisfy a second-order linear ordinary differential equation, whose coefficients are all expressed in terms of the recurrence coefficients. By considering the time evolution, we obtain a system of differential-difference equations satisfied by the recurrence coefficients. Finally, we study the asymptotics of the recurrence coefficients when the degrees of the orthogonal polynomials tend to infinity.

math.CA↗

arXiv2024

Asymptotics of the Smallest Eigenvalue Distributions of Freud Unitary Ensembles

We consider the smallest eigenvalue distributions of some Freud unitary ensembles, that is, the probabilities that all the eigenvalues of the Hermitian matrices from the ensembles lie in the interval $(t,\infty)$. This problem is related to the Hankel determinants generated by the Freud weights with a jump discontinuity. By using Chen and Ismail's ladder operator approach, we obtain the discrete systems for the recurrence coefficients of the corresponding orthogonal polynomials. This enables us to derive the large $n$ asymptotics of the recurrence coefficients via Dyson's Coulomb fluid approach. We finally obtain the large $n$ asymptotics of the Hankel determinants and that of the probabilities from their relations to the recurrence coefficients and with the aid of some recent results in the literature.

math-ph↗

arXiv2024

Error analysis of a collocation method on graded meshes for nonlocal diffusion problems with weakly singular kernels

Can graded meshes yield more accurate numerical solution than uniform meshes? A time-dependent nonlocal diffusion problem with a weakly singular kernel is considered using collocation method. For its steady-state counterpart, under the sufficiently smooth solution, we first clarify that the standard graded meshes are worse than uniform meshes and may even lead to divergence; instead, an optimal convergence rate arises in so-called anomalous graded meshes. Furthermore, under low regularity solutions, it may suffer from a severe order reduction in (Chen, Qi, Shi and Wu, IMA J. Numer. Anal., 41 (2021) 3145--3174). In this case, conversely, a sharp error estimates appears in standard graded meshes, but offering far less than first-order accuracy. For the time-dependent case, however, second-order convergence can be achieved on graded meshes. The related analysis are easily extended for certain multidimensional problems. Numerical results are provided that confirm the sharpness of the error estimates.

math.NA↗

arXiv2024

On the supporting quasi-hyperplane and separation theorem of geodesic convex sets with applications on Riemannian manifolds

In this paper, we first establish the separation theorem between a point and a locally geodesic convex set and then prove the existence of a supporting quasi-hyperplane at any point on the boundary of the closed locally geodesic convex set on a Riemannian manifold. As applications, some optimality conditions are obtained for optimization problems with constraints on Riemannian manifolds.

math.OC↗

arXiv2023

Domain adaption and physical constrains transfer learning for shale gas production

Effective prediction of shale gas production is crucial for strategic reservoir development. However, in new shale gas blocks, two main challenges are encountered: (1) the occurrence of negative transfer due to insufficient data, and (2) the limited interpretability of deep learning (DL) models. To tackle these problems, we propose a novel transfer learning methodology that utilizes domain adaptation and physical constraints. This methodology effectively employs historical data from the source domain to reduce negative transfer from the data distribution perspective, while also using physical constraints to build a robust and reliable prediction model that integrates various types of data. The methodology starts by dividing the production data from the source domain into multiple subdomains, thereby enhancing data diversity. It then uses Maximum Mean Discrepancy (MMD) and global average distance measures to decide on the feasibility of transfer. Through domain adaptation, we integrate all transferable knowledge, resulting in a more comprehensive target model. Lastly, by incorporating drilling, completion, and geological data as physical constraints, we develop a hybrid model. This model, a combination of a multi-layer perceptron (MLP) and a Transformer (Transformer-MLP), is designed to maximize interpretability. Experimental validation in China's southwestern region confirms the method's effectiveness.

cs.LG↗

arXiv2023

Ensemble Interpretation: A Unified Method for Interpretable Machine Learning

To address the issues of stability and fidelity in interpretable learning, a novel interpretable methodology, ensemble interpretation, is presented in this paper which integrates multi-perspective explanation of various interpretation methods. On one hand, we define a unified paradigm to describe the common mechanism of different interpretation methods, and then integrate the multiple interpretation results to achieve more stable explanation. On the other hand, a supervised evaluation method based on prior knowledge is proposed to evaluate the explaining performance of an interpretation method. The experiment results show that the ensemble interpretation is more stable and more consistent with human experience and cognition. As an application, we use the ensemble interpretation for feature selection, and then the generalization performance of the corresponding learning model is significantly improved.

cs.LG↗

arXiv2023

Calico Salmon Migration Algorithm: A novel meta-heuristic optimization algorithm

A novel population-based optimization method is proposed in this paper, the Calico Salmon Migration Algorithm (CSMA), which is inspired by the natural behavior of calico salmon during their migration for mating. The CSMA optimization process comprises four stages: selecting the search space by swimming into the river, expanding the search space from the river into the ocean, performing precise search during the migrating process, and breeding new subspecies by the remaining calico salmon population. To evaluate the effectiveness of the new optimizer, we conducted a series of experiments using different optimization problems and compared the results with various optimization algorithms in the literature. The numerical experimental results for benchmark functions demonstrate that the proposed CSMA outperforms other competing optimization algorithms in terms of convergence speed, accuracy, and stability. Furthermore, the Friedman ranking test shows that the CSMA is ranked first among similar algorithms.

math.OC↗

arXiv2023

Asymptotic Properties of Some Freud Polynomials

We study the asymptotic properties of monic orthogonal polynomials (OPs) with respect to some Freud weights when the degree of the polynomial tends to infinity, including the asymptotics of the recurrence coefficients, the nontrivial leading coefficients of the monic OPs, the associated Hankel determinants and the squares of $L^2$-norm of the monic OPs. These results are derived from the combination of the ladder operator approach, Dyson's Coulomb fluid approach and some recent results in the literature.

math.CA↗