Search

With the rapid development of information technology, scientific social networks (SSNs) have become the fastest and most convenient way for researchers to communicate with each other. Many published papers are shared via SSNs every day, resulting in the problem of information overload. How to appropriately recommend personalized and highly valuable papers for researchers is becoming more urgent. However, when recommending papers in SSNs, only a small amount of positive instances are available, leaving a vast amount of unlabelled data, in which negative instances and potential unseen positive instances are mixed together, which naturally belongs to One-Class Collaborative Filtering (OCCF) problem. Therefore, considering the extreme data imbalance and data sparsity of this OCCF problem, a hybrid approach of Social and Content aware One-class Recommendation of Papers in SSNs, termed SCORP, is proposed in this study. Unlike previous approaches recommended to address the OCCF problem, social information, which has been proved playing a significant role in performing recommendations in many domains, is applied in both the profiling of content-based filtering and the collaborative filtering to achieve superior recommendations. To verify the effectiveness of the proposed SCORP approach, a real-life dataset from CiteULike was employed. The experimental results demonstrate that the proposed approach is superior to all of the compared approaches, thus providing a more effective method for recommending papers in SSNs. [ABSTRACT FROM AUTHOR]

Each year, the editorial board of Computational Optimization and Applications selects a paper from the preceding year's publications for the Best Paper Award. This derivative-free algorithm relies on randomly generated directions and is analyzed from a probabilistic viewpoint, leading to complexity guarantees for both deterministic and probabilistic versions of the method. First, following recent developments in nonconvex optimization, complexity results have become increasingly popular in derivative-free optimization [[8]]. [Extracted from the article]

Quantifying the impact of a scholarly paper is of great significance, yet the effect of geographical distance of cited papers has not been explored. In this paper, we examine 30,596 papers published in Physical Review C, and identify the relationship between citations and geographical distances between author affiliations. Subsequently, a relative citation weight is applied to assess the impact of a scholarly paper. A higher-order weighted quantum PageRank algorithm is also developed to address the behavior of multiple step citation flow. Capturing the citation dynamics with higher-order dependencies reveals the actual impact of papers, including necessary self-citations that are sometimes excluded in prior studies. Quantum PageRank is utilized in this paper to help differentiating nodes whose PageRank values are identical. [ABSTRACT FROM AUTHOR]

Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour. [ABSTRACT FROM AUTHOR]

The Semantic Link Network is a general semantic model for modeling the structure and the evolution of complex systems. Various semantic links play different roles in rendering the semantics of complex system. One of the basic semantic links represents cause-effect relation, which plays an important role in representation and understanding. This paper verifies the role of the Semantic Link Network in representing the core of text by investigating the contribution of cause-effect link to representing the core of scientific papers. Research carries out with the following steps: (1) Two propositions on the contribution of cause-effect link in rendering the core of paper are proposed and verified through a statistical survey, which shows that the sentences on cause-effect links cover about 65% of key words within each paper on average. (2) An algorithm based on syntactic patterns is designed for automatically extracting cause-effect link from scientific papers, which recalls about 70% of manually annotated cause-effect links on average, indicating that the result adapts to the scale of data sets. (3) The effects of cause-effect link on four schemes of incorporating cause-effect link into the existing instances of the Semantic Link Network for enhancing the summarization of scientific papers are investigated. The experiments show that the quality of the summaries is significantly improved, which verifies the role of semantic links. The significance of this research lies in two aspects: (1) it verifies that the Semantic Link Network connects the important concepts to render the core of text; and, (2) it provides an evidence for realizing content services such as summarization, recommendation and question answering based on the Semantic Link Network, and it can inspire relevant research on content computing. [ABSTRACT FROM AUTHOR]

Since the proximal gradient method reduces to the standard steepest descent method for the particular case where HT ht , the rate-of-convergence is typically slow (sublinear). In principle, the proximal gradient method has the major advantage that the subproblems (1) can be solved very efficiently (even analytically) for some practically important proximal functions HT ht . The classical proximal gradient method corresponds to the choice HT ht for all I k i with some (penalty or line search parameter) HT ht , whereas HT ht leads to the proximal Newton method, and HT ht with a (limited memory) quasi-Newton approximation of the Hessian is naturally called a (limited memory) proximal quasi-Newton method. [Extracted from the article]

Research paper recommenders emerged over the last decade to ease finding publications relating to researchers’ area of interest. The challenge was not just to provide researchers with very rich publications at any time, any place and in any form but to also offer the right publication to the right researcher in the right way. Several approaches exist in handling paper recommender systems. However, these approaches assumed the availability of the whole contents of the recommending papers to be freely accessible, which is not always true due to factors such as copyright restrictions. This paper presents a collaborative approach for research paper recommender system. By leveraging the advantages of collaborative filtering approach, we utilize the publicly available contextual metadata to infer the hidden associations that exist between research papers in order to personalize recommendations. The novelty of our proposed approach is that it provides personalized recommendations regardless of the research field and regardless of the user’s expertise. Using a publicly available dataset, our proposed approach has recorded a significant improvement over other baseline methods in measuring both the overall performance and the ability to return relevant and useful publications at the top of the recommendation list. [ABSTRACT FROM AUTHOR]

Many results have been obtained when studying scientific papers citations databases in a network perspective. Articles can be ranked according to their current in-degree and their future popularity or citation counts can even be predicted. The dynamical properties of such networks and the observation of the time evolution of their nodes started more recently. This work adopts an evolutionary perspective and proposes an original algorithm for the construction of genealogical trees of scientific papers on the basis of their citation count evolution in time. The fitness of a paper now amounts to its in-degree growing trend and a “dying” paper will suddenly see this trend declining in time. It will give birth and be taken over by some of its most prevalent citing “offspring”. Practically, this might be used to trace the successive published milestones of a research field. [ABSTRACT FROM AUTHOR]

Nowadays, there has been a rapidly increasing number of scientific submissions in multiple research domains. A large number of journals have various acceptance rates, impact factors, and rankings in different publishers. It becomes time-consuming for many researchers to select the most suitable journal to submit their work with the highest acceptance rate. A paper submission recommendation system is more critical for the research community and publishers as it gives scientists another support to complete their submission conveniently. This paper investigates the submission recommendation system for two main research topics: computer science and applied mathematics. Unlike the previous works (Wang et al., 2018; Son et al., 2020) that extract TF–IDF and statistical features as well as utilize numerous machine learning algorithms (logistics regression and multiple perceptrons) for building the recommendation engine, we present an efficient paper submission recommendation algorithm by using different bidirectional transformer encoders and the Mixture of Transformer Encoders technique. We compare the performance between our methodology and other approaches by one dataset from Wang et al. (2018) with 14012 papers in computer science and another dataset collected by us with 223,782 articles in 178 Springer applied mathematics journals in terms of top K accuracy (K = 1 , 3 , 5 , 10). The experimental results show that our proposed method extensively outperforms other state-of-the-art techniques with a significant margin in all top K accuracy for both two datasets. We publish all datasets collected and our implementation codes for further references. 1 1 https://github.com/BinhMisfit/PSRMTE. • Bidirectional transformer encoders can improve the performance of the paper submission recommendation system. • The Mixture of Transformer Encoders framework shows the efficiency in the paper submission recommendation problem. • Proposed techniques can surpass other recent techniques on two datasets related. [ABSTRACT FROM AUTHOR]

A linear rate for the decay of the expected squared distance to the solution, HT ht , where HT ht is a positive definite matrix defining the norm, was established as well, for a range of stepsizes HT ht and momentum parameters HT ht . Loizou and Richtárik [[10]] further study the decay of the larger quantity HT ht to zero. [Extracted from the article]

In an iterated non-cooperative game, if all the players act to maximize their individual accumulated payoff, the system as a whole usually converges to a Nash equilibrium that poorly benefits any player. Here we show that such an undesirable destiny is avoidable in an iterated Rock-Paper-Scissors (RPS) game involving two rational players, X and Y. Player X has the option of proactively adopting a cooperation-trap strategy, which enforces complete cooperation from the rational player Y and leads to a highly beneficial and maximally fair situation to both players. That maximal degree of cooperation is achievable in such a competitive system with cyclic dominance of actions may stimulate further theoretical and empirical studies on how to resolve conflicts and enhance cooperation in human societies. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we determine the modularities of asymptotically optimal towers found by Maharaj and Wulftange in 2005. This is also a continuation of the work of Elkies in 2002. [Copyright &y& Elsevier]

This paper introduces the contents of the first of two special issues associated with the 9th International Conference on Computational Methods in Applied Mathematics, which took place from August 29 to September 2, 2022 in Vienna. It comments on the topics and highlights of all twelve papers of the special issue. [ABSTRACT FROM AUTHOR]

This document is a preface to a special issue of the journal Mathematics titled "State-of-the-Art Mathematical Applications in Europe." The special issue features twelve original research papers and one review paper from European researchers and their collaborators in various fields of mathematics. The papers cover topics such as mathematical physics, applied mathematics, algebra, navigation algorithms, decision-making models, Lagrange interpolation polynomials, and nonlinear fractional differential equations. The preface provides a brief overview of each paper and expresses gratitude to the authors and reviewers. The special issue has received significant interest and demonstrates the importance of open access research in applied mathematics. [Extracted from the article]

Fundamental scientific advances can take decades to translate into improvements in human health. Shortening this interval would increase the rate at which scientific discoveries lead to successful treatment of human disease. One way to accomplish this would be to identify which advances in knowledge are most likely to translate into clinical research. Toward that end, we built a machine learning system that detects whether a paper is likely to be cited by a future clinical trial or guideline. Despite the noisiness of citation dynamics, as little as 2 years of postpublication data yield accurate predictions about a paper's eventual citation by a clinical article (accuracy = 84%, F1 score = 0.56; compared to 19% accuracy by chance). We found that distinct knowledge flow trajectories are linked to papers that either succeed or fail to influence clinical research. Translational progress in biomedicine can therefore be assessed and predicted in real time based on information conveyed by the scientific community's early reaction to a paper. [ABSTRACT FROM AUTHOR]

This paper offers a historical review of the evolution of mathematical methods in economics, tracing their development from the earliest attempts in the 18th century to the sophisticated models of the late 20th century. The study begins by examining the initial integration of mathematical techniques into economic thought, highlighting key milestones that shaped the field. Symmetry concepts are naturally embedded in many of these mathematical frameworks, particularly in the balance and equilibrium found in economic models. Symmetry in economics often reflects proportional relationships and equilibrium conditions that are central to both micro- and macroeconomic analyses. Then, the paper elaborates on the progression of economic growth models, including the foundational Solow–Swan model, which introduced the concept of technological progress (knowledge) as a key factor influencing growth. The review also encompasses the Lucas growth model and the Mankiw–Romer–Weil model, both of which incorporate human capital into the growth equation, highlighting its importance in driving economic development. Finally, the paper addresses the Nonneman–Vanhoudt model, which extends the analysis of growth by integrating multiple types of capital, providing a more comprehensive framework for understanding economic dynamics. By documenting these developments, the paper demonstrates the significant role that mathematical modeling has played in advancing economic theory, providing tools to quantitatively analyze complex economic phenomena and driving the discipline towards greater analytical precision and rigor. This analysis emphasizes how symmetry principles, such as balance between inputs and outputs, equilibrium in supply and demand, and proportionality in growth models, underpin many economic theories. [ABSTRACT FROM AUTHOR]

We congratulate the authors for the interesting paper. The reading has been really pleasant and instructive. We discuss briefly only some of the interesting results given in Devroye and James (Stat Methods Appl 2014) with particular attention to evolution problems. The contribution of the results collected in the paper is useful in a more wide class of applications in many areas of applied mathematics. [ABSTRACT FROM AUTHOR]

Currently, digitalization and digital transformation are actively expanding into various areas of human activity, and researchers are identifying urgent problems and offering new solutions regarding digital environments in industry [[1]], economics [[3]], medicine [[5]], ecology [[7]], education [[9]], etc. Conclusions The purpose of this Special Issue was to attract high-quality new papers in the field of applied and computational mathematics for digital environments, offering original solutions to various problems that are relevant and in demand in various fields of human activity. 10.3390/math10224297 21 Demidova L.A. A Novel Approach to Decision-Making on Diagnosing Oncological Diseases Using Machine Learning Classifiers Based on Datasets Combining Known and/or New Generated Features of a Different Nature. I hope that these selected research papers are recognized as important and meaningful by the international scientific community and can form the basis for further research in the field of applied and computational mathematics for digital environments, solving complex problems in various disciplines and application areas. [Extracted from the article]

Abstract: In this short note we point to an error in the proof of a theorem stated in [L. Balková, E. Pelantová, Š. Starosta, On Brlek-Reutenauer conjecture, Theoret. Comput. Sci. 412 (2011) 5649–5655]. By constructing a counterexample, we show that the assertion of the theorem is actually incorrect. Although this theorem is of a technical character, it was used in an argument leading to a corollary of a general interest to the Brlek-Reutenauer conjecture, and thus as a consequence of this note we have that the proof of the mentioned corollary is also flawed. [Copyright &y& Elsevier]

Evaluating the impact of a scholarly article is of great significance and has attracted great attentions. Although citation-based evaluation approaches have been widely used, these approaches face limitations e.g. in identifying anomalous citations patterns. This negligence would inevitably cause unfairness and inaccuracy to the article impact evaluation. In this study, in order to discover the anomalous citations and ensure the fairness and accuracy of research outcome evaluation, we investigate the citation relationships between articles using the following factors: collaboration times, the time span of collaboration, citing times and the time span of citing to weaken the relationship of Conflict of Interest (COI) in the citation network. Meanwhile, we study a special kind of COI, namely suspected COI relationship. Based on the COI relationship, we further bring forward the COIRank algorithm, an innovative scheme for accurately assessing the impact of an article. Our method distinguishes the citation strength, and utilizes PageRank and HITS algorithms to rank scholarly articles comprehensively. The experiments are conducted on the American Physical Society (APS) dataset. We find that about 80.88% articles contain contributed citations by co-authors in 26,366 articles and 75.55% articles among these articles are cited by the authors belonging to the same affiliation, indicating COI and suspected COI should not be ignored for evaluating impact of scientific papers objectively. Moreover, our experimental results demonstrate COIRank algorithm significantly outperforms the state-of-art solutions. The validity of our approach is verified by using the probability of Recommendation Intensity. [ABSTRACT FROM AUTHOR]

A new and simple proof of the main result of the paper 'Laterally closed lattice homomorphisms' by Toumi and Toumi (J Math Anal Appl 324:1178-1194, ) is given following the paper 'Extension of Riesz homomorphisms, I' by Buskes (J Aust Math Soc Ser A 39(1):107-120, ). [ABSTRACT FROM AUTHOR]

This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking. [ABSTRACT FROM AUTHOR]

This document is a special issue of the journal Nonlinear Studies, featuring interdisciplinary perspectives in applied mathematics. It includes articles on consumer behavior, diffusion of innovation, numerical methods, game theory, and optimization, covering domains such as engineering, management, and physics. The papers have undergone peer review and offer original and high-quality research. The document compiles research contributions on reliability analysis, mathematical modeling, differential equations, and optimization problems, with references for further exploration. The authors express gratitude to the contributors and reviewers for their valuable contributions. [Extracted from the article]

Almost all situations that arise in applied mathematics involve uncertainty, inconsistency, and indeterminacy. This can be simultaneously handled by the use of single valued neutrosophic fuzzy sets and single valued neutrosophic fuzzy numbers. In this paper, we propose the operations of addition, subtraction, and scalar multiplication on trapezoidal single valued neutrosophic fuzzy numbers. We introduce some component-wise interval operations on the union of closed bounded intervals. Then we show how this can be used to perform the proposed operations on trapezoidal single valued neutrosophic fuzzy numbers with the help of finite α-cuts, finite β-cuts, finite γ-cuts, and finite δ-cuts, which we define in this paper itself. [ABSTRACT FROM AUTHOR]

In this paper, the author derives an analytical exact form of signum function, which evidently constitutes a fundamental concept of Communication Systems and Control Theory along with digital control systems and is also involved in many other fields of applied mathematics and engineering practices. In particular, this significant function is performed in a simple manner as a finite combination of purely algebraic representations. The novelty of this work when compared to other analytical expressions of this nonlinear function is that the proposed explicit representation is not performed in terms of miscellaneous special functions, such as Bessel functions, error function, and beta function, and also is neither the limit of a function nor the limit of a sequence of functions with a point-wise or uniform convergence. [ABSTRACT FROM AUTHOR]

Integral inequalities with generalized convexity play a vital role in both theoretical and applied mathematics. The theory of integral inequalities is one of the branches of mathematics that is now developing at the quickest rate due to its wide range of applications. We define a new Hermite–Hadamard inequality for the novel class of coordinated ƛ-pre-invex fuzzy number-valued mappings (C-ƛ-pre-invex F N V M s) and examine the idea of C-ƛ-pre-invex F N V M s in this paper. Furthermore, using C-ƛ-pre-invex F N V M s, we construct several new integral inequalities for fuzzy double Riemann integrals. Several well-known results, as well as recently discovered results, are included in these findings as special circumstances. We think that the findings in this work are new and will help to stimulate more research in this area in the future. Additionally, unique choices lead to new outcomes. [ABSTRACT FROM AUTHOR]

Integral inequalities involving exponential convexity are significant in both theoretical and applied mathematics. In this paper, we establish a new Hermite-Hadamard type inequality for the class of exponentially convex functions by using the concept of (α − s) exponentially convex function. Additionally, using the well-known Hermite-Hadamard and Ostrowski inequalities, we establish several new integral inequalities. These newly obtained results contain several well-known results as special cases. Finally, new estimations for the trapezoidal formula have been provided, illustrating the practical applications of the research. [ABSTRACT FROM AUTHOR]

This paper investigated the application of analytical methods, specifically the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM), to solve the fractional Boussinesq equation. Utilizing the Caputo operator to manage fractional derivatives, these semi-analytical approaches provide accurate solutions to complex fractional differential equations. Through convergence analysis and error estimation, the study validated the efficacy of these methods by comparing numerical solutions to known exact solutions. Graphical and tabular representations illustrated the accuracy of the proposed methods, highlighting their performance for varying fractional orders. The findings demonstrated that both MTIM and MRPSM offer reliable, efficient solutions, making them valuable tools for addressing fractional differential systems in fields such as applied mathematics, engineering, and physics. [ABSTRACT FROM AUTHOR]

Copyright of Pamukkale University Journal of Social Sciences Institute / Pamukkale Üniversitesi Sosyal Bilimler Enstitüsü Dergisi is the property of Pamukkale University, Social Sciences Institute and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This is the second part of a two‐paper series that establishes the uniqueness and regularity of a threshold energy wave map that does not scatter in both time directions. Consider the S2‐valued equivariant energy critical wave maps equation on ℝ1+2, with equivariance class k≥4. It is known that every topologically trivial wave map with energy less than twice that of the unique k‐equivariant harmonic map Q→k scatters in both time directions. We study maps with precisely the threshold energy E=2EQ→k. In the first part of the series [15] we gave a refined construction of a threshold wave map that asymptotically decouples into a superposition of two harmonic maps (bubbles), one of which is concentrating in scale. In this paper, we show that this solution is the unique (up to the natural invariances of the equation) two‐bubble wave map. Combined with our earlier work [14] we obtain an exact description of every threshold wave map. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Matrix analysis is a powerful tool in the study of modern phenomena and in the application of mathematics in science, engineering, medicine, economics, physics and other scientific disciplines. The eigenvalue analysis, due to its numerous applications, represents an attractive area of applied mathematics. During the 20th century, various researches on the topic of eigenvalue theory were carried out. Hence the idea of this paper is to give an overview of the history of the origin of this type of problem, as well as its applications, primarily in engineering, which would make this paper useful as a starting point for further studies of these specific problems. [ABSTRACT FROM AUTHOR]

Mathematics, both pure and applied, plays a crucial role in shaping societies and driving advancements in various fields. This research paper explores the impact of pure and applied mathematics on Nigerian society, examining their individual contributions and the synergy that emerges from their interplay. The introduction highlights the importance of mathematics in general and provides a context for understanding its significance in the Nigerian context. The subsequent sections delve into the specific impacts of pure and applied mathematics, focusing on their contributions to Nigerian society. The section on pure mathematics discusses its role in fostering critical thinking, logical reasoning, and problem-solving skills, while also showcasing the accomplishments of Nigerian mathematicians in the global mathematical community. The section on applied mathematics explores its applications in sectors such as finance, telecommunications, and engineering, and its contribution to addressing societal challenges and promoting economic development in Nigeria. The paper further investigates the synergy between pure and applied mathematics, illustrating how abstract mathematical concepts often find unexpected practical applications and how real-world challenges drive theoretical advancements. It emphasizes the collaborative efforts between researchers in both fields, the benefits of interdisciplinary perspectives, and the impact on mathematical education and pedagogy. Lastly, the paper addresses the challenges and future directions of pure and applied mathematics in Nigeria, focusing on infrastructure limitations, shortage of skilled mathematicians, integration of mathematics in industry, and the promotion of women's participation. It proposes strategies such as investment in research infrastructure, strengthening mathematics education, fostering interdisciplinary collaboration, and promoting public awareness and engagement. By addressing these challenges and charting future directions, Nigeria can harness the full potential of mathematics as a transformative force in society. [ABSTRACT FROM AUTHOR]

A formal approach to rephrasing nonlinear filtering of stochastic differential equations is the Kushner setting in applied mathematics and dynamical systems. Thanks to the ability of the Carleman linearization, the 'nonlinear' stochastic differential equation can be equivalently expressed as a finite system of 'bilinear' stochastic differential equations with the augmented state under the finite closure. Interestingly, the novelty of this paper is to embed the Carleman linearization into a stochastic evolution of the Markov process. The nonlinear swing equation is the cornerstone and lays the foundation of the power systems dynamics. To illustrate the Carleman linearization of the Markov process, this paper embeds the Carleman linearization into a nonlinear swing stochastic differential equation. Furthermore, we achieve the nonlinear swing equation filtering in the Carleman setting. Filtering in the Carleman setting has simplified algorithmic procedures. The concerning augmented state accounts for the nonlinearity as well as stochasticity. We show that filtering the nonlinear stochastic swing equation in the Carleman framework is more refined as well as sharper in contrast to the benchmark nonlinear extended Kalman filter (EKF). The Carleman filtering framework reduces approximately three times more conditional mean absolute errors as compared to the benchmark EKF method for the application of machine swing dynamics. This paper suggests the usefulness of the Carleman embedding into the stochastic differential equation to filter the concerning nonlinear stochastic differential system. This paper will interest nonlinear stochastic dynamists exploring and unfolding linearization embedding techniques to their research. [ABSTRACT FROM AUTHOR]

The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999–2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics. [ABSTRACT FROM AUTHOR]