arXiv subjects

Chao Min

Publications and source records attributed to Chao Min.

At least 37 records · Page 2Linked to original sources

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

Has China caught up to the US in AI research? An exploration of mimetic isomorphism as a model for late industrializers

Artificial Intelligence (AI), a cornerstone of 21st-century technology, has seen remarkable growth in China. In this paper, we examine China's AI development process, demonstrating that it is characterized by rapid learning and differentiation, surpassing the export-oriented growth propelled by Foreign Direct Investment seen in earlier Asian industrializers. Our data indicates that China currently leads the USA in the volume of AI-related research papers. However, when we delve into the quality of these papers based on specific metrics, the USA retains a slight edge. Nevertheless, the pace and scale of China's AI development remain noteworthy. We attribute China's accelerated AI progress to several factors, including global trends favoring open access to algorithms and research papers, contributions from China's broad diaspora and returnees, and relatively lax data protection policies. In the vein of our research, we have developed a novel measure for gauging China's imitation of US research. Our analysis shows that by 2018, the time lag between China and the USA in addressing AI research topics had evaporated. This finding suggests that China has effectively bridged a significant knowledge gap and could potentially be setting out on an independent research trajectory. While this study compares China and the USA exclusively, it's important to note that research collaborations between these two nations have resulted in more highly cited work than those produced by either country independently. This underscores the power of international cooperation in driving scientific progress in AI.

cs.AI↗

arXiv2023

Prediction of single well production rate in water-flooding oil fields driven by the fusion of static, temporal and spatial information

It is very difficult to forecast the production rate of oil wells as the output of a single well is sensitive to various uncertain factors, which implicitly or explicitly show the influence of the static, temporal and spatial properties on the oil well production. In this study, a novel machine learning model is constructed to fuse the static geological information, dynamic well production history, and spatial information of the adjacent water injection wells. There are 3 basic modules in this stacking model, which are regarded as the encoders to extract the features from different types of data. One is Multi-Layer Perceptron, which is to analyze the static geological properties of the reservoir that might influence the well production rate. The other two are both LSTMs, which have the input in the form of two matrices rather than vectors, standing for the temporal and the spatial information of the target well. The difference of the two modules is that in the spatial information processing module we take into consideration the time delay of water flooding response, from the injection well to the target well. In addition, we use Symbolic Transfer Entropy to prove the superiorities of the stacking model from the perspective of Causality Discovery. It is proved theoretically and practically that the presented model can make full use of the model structure to integrate the characteristics of the data and the experts' knowledge into the process of machine learning, greatly improving the accuracy and generalization ability of prediction.

cs.LG↗

arXiv2022

Interpretability and causal discovery of the machine learning models to predict the production of CBM wells after hydraulic fracturing

Machine learning approaches are widely studied in the production prediction of CBM wells after hydraulic fracturing, but merely used in practice due to the low generalization ability and the lack of interpretability. A novel methodology is proposed in this article to discover the latent causality from observed data, which is aimed at finding an indirect way to interpret the machine learning results. Based on the theory of causal discovery, a causal graph is derived with explicit input, output, treatment and confounding variables. Then, SHAP is employed to analyze the influence of the factors on the production capability, which indirectly interprets the machine learning models. The proposed method can capture the underlying nonlinear relationship between the factors and the output, which remedies the limitation of the traditional machine learning routines based on the correlation analysis of factors. The experiment on the data of CBM shows that the detected relationship between the production and the geological/engineering factors by the presented method, is coincident with the actual physical mechanism. Meanwhile, compared with traditional methods, the interpretable machine learning models have better performance in forecasting production capability, averaging 20% improvement in accuracy.

cs.LG↗

arXiv2022

Differential and Difference Equations for Recurrence Coefficients of Orthogonal Polynomials with a Singularly Perturbed Laguerre-type Weight

We are concerned with the monic orthogonal polynomials with respect to a singularly perturbed Laguerre-type weight. By using the ladder operator approach, we derive a complicated system of nonlinear second-order difference equations satisfied by the recurrence coefficients. This allows us to derive the large $n$ asymptotic expansions of the recurrence coefficients. In addition, we also obtain a system of differential-difference equations for the recurrence coefficients.

math.CA↗

arXiv2022

Painlevé IV, Chazy II, and Asymptotics for Recurrence Coefficients of Semi-classical Laguerre Polynomials and Their Hankel Determinants

This paper studies the monic semi-classical Laguerre polynomials based on previous work by Boelen and Van Assche \cite{Boelen}, Filipuk et al. \cite{Filipuk} and Clarkson and Jordaan \cite{Clarkson}. Filipuk, Van Assche and Zhang proved that the diagonal recurrence coefficient $α_n(t)$ satisfies the fourth Painlevé equation. In this paper we show that the off-diagonal recurrence coefficient $β_n(t)$ fulfills the first member of Chazy II system. We also prove that the sub-leading coefficient of the monic semi-classical Laguerre polynomials satisfies both the continuous and discrete Jimbo-Miwa-Okamoto $σ$-form of Painlevé IV. By using Dyson's Coulomb fluid approach together with the discrete system for $α_n(t)$ and $β_n(t)$, we obtain the large $n$ asymptotic expansions of the recurrence coefficients and the sub-leading coefficient. The large $n$ asymptotics of the associate Hankel determinant (including the constant term) is derived from its integral representation in terms of the sub-leading coefficient.

math.CA↗

arXiv2022

Global and Local Scaling Limits for Linear Eigenvalue Statistics of Jacobi $β$-Ensembles

We study the moment-generating functions (MGF) for linear eigenvalue statistics of Jacobi unitary, symplectic and orthogonal ensembles. By expressing the MGF as Fredholm determinants of kernels of finite rank, we show that the mean and variance of the suitably scaled linear statistics in these Jacobi ensembles are related to the sine kernel in the bulk of the spectrum, whereas they are related to the Bessel kernel at the (hard) edge of the spectrum. The relation between the Jacobi symplectic/orthogonal ensemble (JSE/JOE) and the Jacobi unitary ensemble (JUE) is also established.

math-ph↗

arXiv2022

Team formation and team performance: The balance between team freshness and repeat collaboration

Incorporating fresh members in teams is considered a pathway to team creativity. However, whether freshness improves team performance or not remains unclear, as well as the optimal involvement of fresh members for team performance. This study uses a group of authors on the byline of a publication as a proxy for a scientific team. We extend an indicator, i.e., team freshness, to measure the extent to which a scientific team incorporates new members, by calculating the fraction of new collaboration relations established within the team. Based on more than 43 million scientific publications covering more than a half-century of research from Microsoft Academic Graph, this study provides a holistic picture of the current development of team freshness by outlining the temporal evolution of freshness, and its disciplinary distribution. Subsequently, using a multivariable regression approach, we examine the association between team freshness and papers'short-term and long-term citations.The major findings are as follows: (1)team freshness in scientific teams has been increasing in the past half-century; (2)there exists an inverted-U-shaped association between team freshness and papers' citations in all the disciplines and in different periods;(3)the inverted-U-shaped relationship between team freshness and papers' citations is only found in small teams, while, in large teams, team freshness is significantly positively related to papers' citations.

cs.DL↗

arXiv2022

Hankel Determinant and Orthogonal Polynomials for a Perturbed Gaussian Weight: from Finite $n$ to Large $n$ Asymptotics

We study the monic polynomials orthogonal with respect to a symmetric perturbed Gaussian weight $$ w(x;t):=\mathrm{e}^{-x^2}\left(1+t\: x^2\right)^λ,\qquad x\in \mathbb{R}, $$ where $t> 0,\;λ\in \mathbb{R}$. This weight is related to the single-user MIMO systems in information theory. It is shown that the recurrence coefficient $β_n(t)$ is related to a particular Painlevé V transcendent, and the sub-leading coefficient $\mathrm{p}(n,t)$ satisfies the Jimbo-Miwa-Okamoto $σ$-form of the Painlevé V equation. Furthermore, we derive the second-order difference equations satisfied by $β_n(t)$ and $\mathrm{p}(n,t)$, respectively. This enables us to obtain the large $n$ full asymptotic expansions for $β_n(t)$ and $\mathrm{p}(n,t)$ with the aid of Dyson's Coulomb fluid approach. We also consider the Hankel determinant $D_n(t)$, generated by the perturbed Gaussian weight. It is found that $H_n(t)$, a quantity allied to the logarithmic derivative of $D_n(t)$, can be expressed in terms of $β_n(t)$ and $\mathrm{p}(n,t)$. Based on this result, we obtain the large $n$ asymptotic expansion of $H_n(t)$ and then that of the Hankel determinant $D_n(t)$.

math-ph↗

arXiv2021

Pandemics are catalysts of scientific novelty: Evidence from COVID-19

Scientific novelty drives the efforts to invent new vaccines and solutions during the pandemic. First-time collaboration and international collaboration are two pivotal channels to expand teams' search activities for a broader scope of resources required to address the global challenge, which might facilitate the generation of novel ideas. Our analysis of 98,981 coronavirus papers suggests that scientific novelty measured by the BioBERT model that is pre-trained on 29 million PubMed articles, and first-time collaboration increased after the outbreak of COVID-19, and international collaboration witnessed a sudden decrease. During COVID-19, papers with more first-time collaboration were found to be more novel and international collaboration did not hamper novelty as it had done in the normal periods. The findings suggest the necessity of reaching out for distant resources and the importance of maintaining a collaborative scientific community beyond nationalism during a pandemic.

cs.DL↗

arXiv2021

Semi-classical Jacobi Polynomials, Hankel Determinants and Asymptotics

We study orthogonal polynomials and Hankel determinants generated by a symmetric semi-classical Jacobi weight. By using the ladder operator technique, we derive the second-order nonlinear difference equations satisfied by the recurrence coefficient $β_n(t)$ and the sub-leading coefficient $\mathrm{p}(n,t)$ of the monic orthogonal polynomials. This enables us to obtain the large $n$ asymptotics of $β_n(t)$ and $\mathrm{p}(n,t)$ based on the result of Kuijlaars et al. [Adv. Math. \textbf{188} (2004) 337-398]. In addition, we show the second-order differential equation satisfied by the orthogonal polynomials, with all the coefficients expressed in terms of $β_n(t)$. From the $t$ evolution of the auxiliary quantities, we prove that $β_n(t)$ satisfies a second-order differential equation and $R_n(t)=2n+1+2α-2t(β_n(t)+β_{n+1}(t))$ satisfies a particular Painlevé V equation under a simple transformation. Furthermore, we show that the logarithmic derivative of the associated Hankel determinant satisfies both the second-order differential and difference equations. The large $n$ asymptotics of the Hankel determinant is derived from its integral representation in terms of $β_n(t)$ and $\mathrm{p}(n,t)$.

math.CA↗

arXiv2021

Differential, Difference and Asymptotic Relations for Pollaczek-Jacobi Type Orthogonal Polynomials and Their Hankel Determinants

In this paper, we study the orthogonal polynomials with respect to a singularly perturbed Pollaczek-Jacobi type weight $$ w(x,t):=(1-x^2)^α\mathrm{e}^{-\frac{t}{1-x^{2}}},\qquad x\in[-1,1],\;\;α>0,\;\;t>0. $$ By using the ladder operator approach, we establish the second-order difference equations satisfied by the recurrence coefficient $β_n(t)$ and the sub-leading coefficient $\mathrm{p}(n,t)$ of the monic orthogonal polynomials, respectively. We show that the logarithmic derivative of $β_n(t)$ can be expressed in terms of a particular Painlevé V transcendent. The large $n$ asymptotic expansions of $β_n(t)$ and $\mathrm{p}(n,t)$ are obtained by using Dyson's Coulomb fluid method together with the related difference equations. Furthermore, we study the associated Hankel determinant $D_n(t)$ and show that a quantity $σ_n(t)$, allied to the logarithmic derivative of $D_n(t)$, can be expressed in terms of the $σ$-function of a particular Painlevé V. The second-order differential and difference equations for $σ_n(t)$ are also obtained. In the end, we derive the large $n$ asymptotics of $σ_n(t)$ and $D_n(t)$ from their relations with $β_n(t)$ and $\mathrm{p}(n,t)$.

math.CA↗

arXiv2021

References of References: How Far is the Knowledge Ancestry

Scientometrics studies have extended from direct citations to high-order citations, as simple citation count is found to tell only part of the story regarding scientific impact. This extension is deemed to be beneficial in scenarios like research evaluation, science history modeling, and information retrieval. In contrast to citations of citations (forward citation generations), references of references (backward citation generations) as another side of high-order citations, is relatively less explored. We adopt a series of metrics for measuring the unfolding of backward citations of a focal paper, tracing back to its knowledge ancestors generation by generation. Two sub-fields in Physics are subject to such analysis on a large-scale citation network. Preliminary results show that (1) most papers in our dataset can be traced to their knowledge ancestry; (2) the size distribution of backward citation generations presents a decreasing-and-then-increasing shape; and (3) citations more than one generation away are still relevant to the focal paper, from either a forward or backward perspective; yet, backward citation generations are higher in topic relevance to the paper of interest. Furthermore, the backward citation generations shed lights for literature recommendation, science evaluation, and sociology of science studies.

cs.DL↗

arXiv2020

Painlevé V and the Hankel Determinant for a Singularly Perturbed Jacobi Weight

We study the Hankel determinant generated by a singularly perturbed Jacobi weight $$ w(x,t):=(1-x^2)^α\mathrm{e}^{-\frac{t}{x^{2}}},\;\;\;\;\;\;x\in[-1,1],\;\;α>0,\;\;t\geq 0. $$ If $t=0$, it is reduced to the classical symmetric Jacobi weight. For $t>0$, the factor $\mathrm{e}^{-\frac{t}{x^{2}}}$ induces an infinitely strong zero at the origin. This Hankel determinant is related to the Wigner time-delay distribution in chaotic cavities. In the finite $n$ dimensional case, we obtain two auxiliary quantities $R_n(t)$ and $r_n(t)$ by using the ladder operator approach. We show that the Hankel determinant has an integral representation in terms of $R_n(t)$, where $R_n(t)$ is closely related to a particular Painlevé V transcendent. Furthermore, we derive a second-order nonlinear differential equation and also a second-order difference equation for the logarithmic derivative of the Hankel determinant. This quantity can be expressed in terms of the Jimbo-Miwa-Okamoto $σ$-function of a particular Painlevé V. Then we consider the asymptotics of the Hankel determinant under a suitable double scaling, i.e. $n\rightarrow\infty$ and $t\rightarrow 0$ such that $s=2n^2 t$ is fixed. Based on previous results by using the Coulomb fluid method, we obtain the large $s$ and small $s$ asymptotic behaviors of the scaled Hankel determinant, including the constant term in the asymptotic expansion.

math-ph↗

arXiv2020

Citation Cascade and the Evolution of Topic Relevance

Citation analysis, as a tool for quantitative studies of science, has long emphasized direct citation relations, leaving indirect or high order citations overlooked. However, a series of early and recent studies demonstrate the existence of indirect and continuous citation impact across generations. Adding to the literature on high order citations, we introduce the concept of a citation cascade: the constitution of a series of subsequent citing events initiated by a certain publication. We investigate this citation structure by analyzing more than 450,000 articles and over 6 million citation relations. We show that citation impact exists not only within the three generations documented in prior research, but also in much further generations. Still, our experimental results indicate that two to four generations are generally adequate to trace a work's scientific impact. We also explore specific structural properties such as depth, width, structural virality, and size, which account for differences among individual citation cascades. Finally, we find evidence that it is more important for a scientific work to inspire trans domain (or indirectly related domain) works than to receive only intra domain recognition in order to achieve high impact. Our methods and findings can serve as a new tool for scientific evaluation and the modeling of scientific history.

cs.SI↗

arXiv2020

Asymptotics of the Largest Eigenvalue Distribution of the Laguerre Unitary Ensemble

We study the probability that all the eigenvalues of $n\times n$ Hermitian matrices, from the Laguerre unitary ensemble with the weight $x^γ\mathrm{e}^{-4nx},\;x\in[0,\infty),\;γ>-1$, lie in the interval $[0,α]$. By using previous results for finite $n$ obtained by the ladder operator approach of orthogonal polynomials, we derive the large $n$ asymptotics of the largest eigenvalue distribution function with $α$ ranging from 0 to the soft edge. In addition, at the soft edge, we compute the constant conjectured by Tracy and Widom [Commun. Math. Phys. 159 (1994), 151-174], later proved by Deift, Its and Krasovsky [Commun. Math. Phys. 278 (2008), 643-678]. Our results are reduced to those of Deift et al. when $γ=0$.

math-ph↗

arXiv2019

Painlevé VI, Painlevé III and the Hankel Determinant Associated with a Degenerate Jacobi Unitary Ensemble

This paper studies the Hankel determinant generated by a perturbed Jacobi weight, which is closely related to the largest and smallest eigenvalue distribution of the degenerate Jacobi unitary ensemble. By using the ladder operator approach for the orthogonal polynomials, we find that the logarithmic derivative of the Hankel determinant satisfies a nonlinear second-order differential equation, which turns out to be the Jimbo-Miwa-Okamoto $σ$-form of the Painlevé VI equation by a translation transformation. We also show that, after a suitable double scaling, the differential equation is reduced to the Jimbo-Miwa-Okamoto $σ$-form of the Painlevé III. In the end, we obtain the asymptotic behavior of the Hankel determinant as $t\rightarrow1^{-}$ and $t\rightarrow0^{+}$ in two important cases, respectively.

math-ph↗

arXiv2019

Linear Statistics of Random Matrix Ensembles at the Spectrum Edge Associated with the Airy Kernel

In this paper, we study the large $N$ behavior of the moment-generating function (MGF) of the linear statistics of $N\times N$ Hermitian matrices in the Gaussian unitary, symplectic, orthogonal ensembles (GUE, GSE, GOE) and Laguerre unitary, symplectic, orthogonal ensembles (LUE, LSE, LOE) at the edge of the spectrum. From the finite $N$ Fredholm determinant expression of the MGF of the linear statistics, we find the large $N$ asymptotics of the MGF associated with the Airy kernel in these Gaussian and Laguerre ensembles. Then we obtain the mean and variance of the suitably scaled linear statistics. We show that there is an equivalence between the large $N$ behavior of the MGF of the scaled linear statistics in Gaussian and Laguerre ensembles, which leads to the statistical equivalence between the mean and variance of suitably scaled linear statistics in Gaussian and Laguerre ensembles. In the end, we use the Coulomb fluid method to obtain the mean and variance of another type of linear statistics in GUE, which reproduces the result of Basor and Widom.

math-ph↗