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QR decomposition is widely used for solving the least squares problem. However, existing materials about it may be too abstract for non-mathematicians, especially STEM students, and/or require serious background in linear algebra. The paper describes theoretical background and examples of GNU Octave compatible MATLAB scripts that give relatively simple but complete explanations about how to use QR decomposition for the least squares problem solution. Only basic knowledge of linear algebra and calculus are required. Both Givens rotations and Householder reflections usage for the linear least squares problem were considered. It was shown that the algorithm based on Givens rotations is even easier to program than explicit formation of the normal equations with subsequent usage of Gaussian elimination.

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]

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]

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]

This note tries to answer issues raised in Bhardwaj and Kumar (J Optim Theory Appl 163(2): 685-696, 2014). The research summarizes that the results obtained in Khan et al. (J Optim Theory Appl 159: 536-546, 2013) are sound and correct and it fulfills all the necessary requirements of its scope and objectives. [ABSTRACT FROM AUTHOR]

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]

Recent rank-based attacks have reduced the security of Rainbow, which is one of the multi-layer UOV signatures, below the NIST security requirements by speeding up iterative kernel-finding operations using classical mathematics techniques. If quantum algorithms are applied to perform these iterative operations, the rank-based attacks may be more threatening to multi-layer UOV, including Rainbow. In this paper, we propose a quantum rectangular MinRank attack called the Q-rMinRank attack, the first quantum approach to key recovery attacks on multi-layer UOV signatures. Our attack is a general model applicable to multi-layer UOV signature schemes, and in this paper, we provide examples of its application to Rainbow and the Korean TTA standard, HiMQ. We design two quantum oracle circuits to find the kernel in consideration of the depth-width trade-off of quantum circuits. One is to reduce the width of the quantum circuits using qubits as a minimum, and the other is to reduce the depth using parallelization instead of using a lot of qubits. By designing quantum circuits to find kernels with fewer quantum resources and complexity by adding mathematical techniques, we achieve quadratic speedup for the MinRank attack to recover the private keys of multi-layer UOV signatures. We also estimate quantum resources for the designed quantum circuits and analyze quantum complexity based on them. The width-optimized circuit recovers the private keys of Rainbow parameter set V with only 1089 logical qubits. The depth-optimized circuit recovers the private keys of Rainbow parameter set V with a quantum complexity of 2 174 , which is lower than the complexity of 2 221 recovering the secret key of AES-192, which provides the same security level as parameter set III. [ABSTRACT FROM AUTHOR]

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]

Purpose. As a scientific field, bioinformatics has drawn remarkable attention from various fields, such as information technology, mathematics, and modern biological sciences, in recent years. The topic models originating from the field of natural language processing have become the focus of attention with the rapid accumulation of biological datasets. Thus, this research is aimed at modeling the topic content of the bioinformatics literature presented by Iranian researchers in the Scopus Citation Database. Methodology. This research was a descriptive-exploratory study, and the studied population included 3899 papers indexed in the Scopus database, which had been indexed in this database until March 9, 2022. The topic modeling was then performed on the abstracts and titles of the papers. A combination of LDA and TF-IDF was utilized for topic modeling. Findings. The data analysis with topic modeling resulted in identifying seven main topics "Molecular Modeling," "Gene Expression," "Biomarker," "Coronavirus," "Immunoinformatics," "Cancer Bioinformatics," and "Systems Biology." Moreover, "Systems Biology" and "Coronavirus" had the largest and smallest clusters, respectively. Conclusion. The present investigation demonstrated an acceptable performance for the LDA algorithm in classifying the topics included in this field. The extracted topic clusters indicated excellent consistency and topic connection with each other. [ABSTRACT FROM AUTHOR]

This research aims to improve the rationality and intelligence of AUTOMATICALLY HIGHER MATHEMATICALLY EXAM SYSTEM (AHMES) through some AI algorithms. AHMES is an intelligent and high-quality higher math examination solution for the Department of Computer Engineering at Pai Chai University. This research redesigned the difficulty system of AHMES and used some AI algorithms for initialization and continuous adjustment. This paper describes the multiple linear regression algorithm involved in this research and the AHMES learning (AL) algorithm improved by the Q-learning algorithm. The simulation test results of the upgraded AHMES show the effectiveness of these algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a modular approach to motion planning with provable stability guarantees for robots that move through changing environments via periodic locomotion behaviors. We focus on dynamic walkers as a paradigm for such systems, although the tools developed in this paper can be used to support general compositional approaches to robot motion planning with dynamic movement primitives (DMPs). By formulating the planning process as a switching system with multiple equilibria (SSME), we prove that the system's evolution remains within explicitly characterized trapping regions in the state space under suitable constraints on the frequency of switching among the DMPs. These conditions encapsulate the low-level stability limitations in a form that can be easily communicated to the planner. Furthermore, we show how the available primitives can be safely composed online in a receding horizon manner to enable the robot to react to moving obstacles. The proposed framework can be applied in a wide class of 3D bipedal walking models, and offers a modular approach for integrating readily available low-level locomotion control and high-level planning methods. [ABSTRACT FROM AUTHOR]

This paper investigates numerical solutions of pseudomontone variational inequality problems in real Hilbert spaces. Two new algorithms based on the celebrated extragradient method are introduced. Under suitable conditions, it is proved that the two algorithms achieve weak convergence and linear convergence rates. The results extend and improve upon related works in the literature on the associated extragradient algorithms. [ABSTRACT FROM AUTHOR]

The concept of contraction mappings plays a significant role in mathematics, particularly in the study of fixed points and the existence of solutions for various equations. In this study, we described two types of enriched contractions: enriched F-contraction and enriched F'-contraction associated with u-fold averaged mapping, which are involved with Kirk's iterative technique with order u. The contractions extracted from this paper generalized and unified many previously common super contractions. Furthermore, u-fold averaged mappings can be seen as a more general form of both averaged mappings and double averaged mappings. Moreover, we demonstrated that the ufold averaged mapping with enriched contractions has a unique fixed point. Our work examined the necessary conditions for the u-fold averaged mapping and weak enriched contractions to have equal sets of fixed points. Additionally, we illustrated that an appropriate Kirk's iterative algorithm can effectively approximate a fixed point of a u-fold averaged mapping as well as the two enriched contractions. Also, we delved into the well-posedness, limit shadowing property, and Ulam-Hyers stability of the u-fold averaged mapping. Furthermore, we established necessary conditions that guaranteed the periodic point property for each of the illustrated strengthened contractions. To underscore the generality of our findings, we presented several examples that aligned with comparable results found in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, an operational matrix method based on the Bell polynomials has been presented to find approximate solutions of highorder Volterra integro-difierential equations. This method uses a simple computational manner to obtain a quite acceptable approximate solution. The main characteristic behind this method lies in the fact that on the one hand, the problem will be reduced to a system of algebraic equations and on the other hand, the effciency and accuracy of the Bell polynomials for solving these equations are acceptable. The convergence analysis of this method will be shown by preparing some theorems. Moreover, we will obtain an estimation of the error bound for this algorithm. Finally, some examples are presented to illustrate the applicability, eficiency and accuracy of this scheme in comparison with some other well-known methods such as Legendre, Bernoulli, Taylor and Bessel polynomial algorithms. [ABSTRACT FROM AUTHOR]

This article investigates subject-related research metrics from the most popular scientometrics platforms with the capability of citation count. Quantitative analyses have been carried out to determine the most- to the least-cited subject areas to indicate the most active and dynamic fields in research. Subject areas are classified based on statistical analyses and the number of citations received in the period of search. Numerous articles were analyzed from top-ranked journals in all research fields covered by SCImago journal classification. A comprehensive data set was generated in 27 research subject areas, including 313 subject categories and 81 high-ranked journals. Results showed that the highest number of citations were related to the sciences and science-related subject areas. The subject areas of computer science and mathematics had the lowest research metrics and the smallest number of highly cited publications. Web of Science performed better than Scopus for subject-related evaluations. Analysis of frequency data showed that Google Scholar cited fewer papers for low-cited publications than did Scopus or Web of Science. For highly cited publications, however, Google Scholar was found to have better performance. Web of Science showed the best consistency in citation coverage in most of the investigated subject areas. [ABSTRACT FROM AUTHOR]

The higher-order guaranteed lower eigenvalue bounds of the Laplacian in the recent work by Carstensen et al. (Numer Math 149(2):273–304, 2021) require a parameter C st , 1 that is found not robust as the polynomial degree p increases. This is related to the H 1 stability bound of the L 2 projection onto polynomials of degree at most p and its growth C st, 1 ∝ (p + 1) 1 / 2 as p → ∞ . A similar estimate for the Galerkin projection holds with a p-robust constant C st , 2 and C st , 2 ≤ 2 for right-isosceles triangles. This paper utilizes the new inequality with the constant C st , 2 to design a modified hybrid high-order eigensolver that directly computes guaranteed lower eigenvalue bounds under the idealized hypothesis of exact solve of the generalized algebraic eigenvalue problem and a mild explicit condition on the maximal mesh-size in the simplicial mesh. A key advance is a p-robust parameter selection. The analysis of the new method with a different fine-tuned volume stabilization allows for a priori quasi-best approximation and improved L 2 error estimates as well as a stabilization-free reliable and efficient a posteriori error control. The associated adaptive mesh-refining algorithm performs superior in computer benchmarks with striking numerical evidence for optimal higher empirical convergence rates. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of finding a solution of a pseudomonotone variational inequality problem with the constraints of fixed points of a finite family of demicontractive multivalued mappings. We introduce a new generalized viscosity inertial Tseng's extragradient method which uses self-adaptive step sizes. Unlike some existing results in this direction, we prove our strong convergence theorems without the sequentially weakly continuity condition of the pseudomonotone operator and without the knowledge of Lipschitz constants. Moreover, our strong convergence results do not follow the conventional "two cases" approach, which was often employed in proving strong convergence. Finally, we apply our result to convex minimization problems and present several numerical experiments to illustrate the performance of the proposed algorithms in comparison with other existing methods in the literature. [ABSTRACT FROM AUTHOR]

A given special case of NP-complete scheduling problem can be approximated by solving a special case of similar problem with the same precedence graph. We construct a metric space over a set of special cases of this problem and consider the statistical relationship between distance between a pair of special cases of the under consideration and the average error of the approximated solution. Sethi, Gabow, Coffman's and Fujii's algorithms for this problem are used. It is shown that the absolute and the relative error of the objective function decreases over the density of a graph with a fixed number of jobs. In general case, relative non-zero error value increases with the number of jobs. [ABSTRACT FROM AUTHOR]

Map-matching technology is a key and difficult technology in the development of vehicle navigation systems. Only by correctly identifying the road segment on which the vehicle is traveling can the navigation system make the right decision. At the same time, the complexity of the road network structure and a variety of error factors have introduced great challenges to map matching and have attracted the attention of many researchers as well. This paper analyzes various map-matching algorithms, determines that the key to the matching performance is the junction matching, performs an in-depth study on the junction-matching problem, and puts forward the junction decision domain model. The model mainly involves information regarding the width of the road segment, the angle between two road segments, the accuracy of GPS and the accuracy of the road network. In this paper, we use this model to improve the map-matching algorithm based on a hidden Markov model (HMM). The experimental results show that the improved matching algorithm can effectively reduce the error rate of junction matching and improve the matching performance of a navigation system. [ABSTRACT FROM AUTHOR]

This paper, based on differential privacy protecting K-means clustering algorithm, realizes privacy protection by adding data-disturbing Laplace noise to cluster center point. In order to solve the problem of Laplace noise randomness which causes the center point to deviate, especially when poor availability of clustering results appears because of small privacy budget parameters, an improved differential privacy protecting K-means clustering algorithm was raised in this paper. The improved algorithm uses the contour coefficients to quantitatively evaluate the clustering effect of each iteration and add different noise to different clusters. In order to be adapted to the huge number of data, this paper provides an algorithm design in MapReduce Framework. Experimental finding shows that the new algorithm improves the availability of the algorithm clustering results under the condition of ensuring individual privacy without significantly increasing its operating time. [ABSTRACT FROM AUTHOR]

Recently, computational Grids have proven to be a good solution for processing large-scale, computation intensive problems. However, the heterogeneity, dynamics of resources and diversity of applications requirements have always been important factors affecting their performance. In response to these challenges, this work first builds a Grid job scheduling architecture that can dynamically monitor Grid computing center resources and make corresponding scheduling decisions. Second, a Grid job model is proposed to describe the application requirements. Third, this paper studies the characteristics of commercial interconnection networks used in Grids and forecast job transmission time. Fourth, this paper proposes an application-aware job scheduling mechanism (AJSM) that includes periodic scheduling flow and a heuristic application-aware deadline constraint job scheduling algorithm. The rigorous performance evaluation results clearly demonstrate that the proposed application-aware job scheduling mechanism can successful schedule more Grid jobs than the existing algorithms. For successful scheduled jobs, our proposed AJSM method is the best algorithm for job average processing time and makespan. [ABSTRACT FROM AUTHOR]

In this paper we consider finding a second-order stationary point (SOSP) of nonconvex equality constrained optimization when a nearly feasible point is known. In particular, we first propose a new Newton-conjugate gradient (Newton-CG) method for finding an approximate SOSP of unconstrained optimization and show that it enjoys a substantially better complexity than the Newton-CG method in [C. W. Royer, M. O'Neill, and S. J. Wright, Math. Program., 180 (2020), pp. 451-488]. We then propose a Newton-CG based augmented Lagrangian (AL) method for finding an approximate SOSP of nonconvex equality constrained optimization, in which the proposed Newton-CG method is used as a subproblem solver. We show that under a generalized linear independence constraint qualification (GLICQ), our AL method enjoys a total inner iteration complexity of O(ε7/peration complexity of O(ε7/2 min\{ n, ε3/4\}) for finding an (ε, ε)-SOSP of nonconvex equality constrained optimization with high probability, which are significantly better than the ones achieved by the proximal AL method in [Y. Xie and S. J. Wright, J. Sci. Comput., 86 (2021), pp. 1-30]. In addition, we show that it has a total inner iteration complexity of O(ε11/2) and an operation complexity of O(ε11/2 min\{ n, ε5/4\}) when the GLICQ does not hold. To the best of our knowledge, all the complexity results obtained in this paper are new for finding an approximate SOSP of nonconvex equality constrained optimization with high probability. Preliminary numerical results also demonstrate the superiority of our proposed methods over the other competing algorithms. [ABSTRACT FROM AUTHOR]

[M. Ma, The connectivity of exchanged hypercubes, Discrete Math., Algorithms Appl. 2(2) (2010) 213–220.] proved that the vertex connectivity and the edge connectivity of the exchanged hypercube are each equal to the minimum degree of the graph. This paper presents a proof of that result, which is substantially simpler and more intuitive. [ABSTRACT FROM AUTHOR]

Rational functions have deep system-theoretic significance. They represent the natural way of modeling linear dynamical systems in the frequency (Laplace) domain. Using rational functions, the goal of this paper to compute models that match (interpolate) given data sets of measurements. In this paper, the authors show that using special rational orthonormal systems, the Malmquist-Takenaka systems, it is possible to write the rational interpolant r(n,m), for n=N-1,m=N using only N sampling nodes (instead of 2N nodes) if the interpolating nodes are in the complex unit circle or on the upper half-plane. Moreover, the authors prove convergence results related to the rational interpolant. They give an efficient algorithm for the determination of the rational interpolant. [ABSTRACT FROM AUTHOR]

In this paper, a reliable new scheme is presented based on combining Reproducing Kernel Method (RKM) with a practical technique for the nonlinear problem to solve the System of Singularly Perturbed Boundary Value Problems (SSPBVP). The Gram-Schmidt orthogonalization process is removed in the present RKM. However, we provide error estimation for the approximate solution and its derivative. Based on the present algorithm in this paper, can also solve linear problem. Several numerical examples demonstrate that the present algorithm does have higher precision. [ABSTRACT FROM AUTHOR]

This paper proposes SAR imaging algorithm with largest coherence based on the existing SAR imaging algorithm. The basic idea of SAR imaging algorithm in imaging processing is that output signal can have maximum signal-to-noise ratio (SNR) by using the optimal imaging parameters. Traditional imaging algorithm can acquire the best focusing effect, but would bring the decoherence phenomenon in subsequent interference process. Algorithm proposed in this paper is that SAR echo adopts consistent imaging parameters in focusing processing. Although the SNR of the output signal is reduced slightly, their coherence is ensured greatly, and finally the interferogram with high quality is obtained. In this paper, two scenes of Envisat ASAR data in Zhangbei are employed to conduct experiment for this algorithm. Compared with the interferogram from the traditional algorithm, the results show that this algorithm is more suitable for SAR interferometry (InSAR) research and application. [ABSTRACT FROM AUTHOR]

In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction, to solve semi-definite programs (SDPs) is shown by (i) assuming that the given SDP is nondegenerate and making modifications to these algorithms [Kojima et al. Local convergence of predictor–corrector infeasible-interior-point algorithms for SDPs and SDLCPs, Math. Program. Ser. A 80 (1998), pp. 129–160], or (ii) considering special classes of SDPs, such as the class of linear semi-definite feasibility problems (LSDFPs) and requiring the initial iterate to the algorithm to satisfy certain conditions [Sim, Superlinear convergence of an infeasible predictor–corrector path-following interior point algorithm for a semidefinite linear complementarity problem using the Helmberg–Kojima–Monteiro direction, SIAM J. Optim. 21 (2011), pp. 102–126], [Sim, Interior point method on semi-definite linear complementarity problems using the Nesterov-Todd (NT) search direction: Polynomial complexity and local convergence, Comput. Optim. Appl. 74 (2019), pp. 583–621]. Otherwise, these algorithms are not easy to implement even though they are shown to have polynomial iteration complexities and superlinear convergence [Luo et al. Superlinear convergence of a symmetric primal–dual path following algorithm for semidefinite programming, SIAM J. Optim. 8 (1998), pp. 59–81]. The conditions in [Sim, Superlinear convergence of an infeasible predictor–corrector path-following interior point algorithm for a semidefinite linear complementarity problem using the Helmberg–Kojima–Monteiro direction, SIAM J. Optim. 21 (2011), pp. 102–126], [Sim, Interior point method on semi-definite linear complementarity problems using the Nesterov-Todd (NT) search direction: Polynomial complexity and local convergence, Comput. Optim. Appl. 74 (2019), pp. 583–621] that the initial iterate to the algorithm is required to satisfy to have superlinear convergence when solving LSDFPs however are not practical. In this paper, we propose a practical initial iterate to an implementable infeasible interior point algorithm that guarantees superlinear convergence when the algorithm is used to solve the homogeneous feasibility model of an LSDFP. [ABSTRACT FROM AUTHOR]

Being inspired by the biological eye, event camera is a novel asynchronous technology that poses a paradigm shift in acquisition of visual information. This paradigm enables event cameras to capture pixel-size fast motions much more naturally compared to classical cameras.In this paper, we present a new asynchronous event-driven algorithm for detection of high-frequency pixel-size periodic signals using an event camera. Development of such new algorithms to efficiently process the asynchronous information of event cameras is essential to utilize its special properties and potential, and being a main challenge in the research community.It turns out that this algorithm, which was developed in order to satisfy the new paradigm, is related to an untreated theoretical problem in probability: Let 0 ≤ τ1 ≤ τ2 ≤⋯ ≤ τm ≤ 1 originated from an unknown distribution. Let also 휖,δ ∈ ℝ, and d ∈ ℕ. What can be said about the probability Φ(m,d) of having more than d adjacent τi-s pairs that the distance between them is δ, up to an error 휖? This problem, which reminds the area of order statistic, shows how the new visualization paradigm is also an opportunity to develop new areas and problems in mathematics. [ABSTRACT FROM AUTHOR]

To improve the convergence of the gradient iterative (GI) algorithm and the Jacobi‐gradient iterative (JGI) algorithm [Bayoumi, Appl Math Inf Sci, 2021], a shift‐splitting Jacobi‐gradient iterative (SSJGI) algorithm for solving the matrix equation A풱−풱‾B=C is presented in this paper, which is based on the splitting of the coefficient matrices. The proposed algorithm converges to the exact solution for any initial value with some conditions. To demonstrate the effectiveness of the SSJGI algorithm and to compare it to the GI algorithm and the JGI algorithm [Bayoumi, Appl Math Inf Sci, 2021], numerical examples are provided. [ABSTRACT FROM AUTHOR]

Simple Summary: Cancer is basically a tough condition on a patient's body where cell grows uncontrollably. Normal cells are affected, which destroys the health of the patient. The main problem in cancer is spreading from one part to another. Therefore, the mathematical modeling of cancerous tumors integrates to check overall stability. A novel approach is introduced such as Bernstein polynomial with combination of genetic algorithm, sliding mode controller, and synergetic control. The proposed solution has easily eliminated cancerous cells within five days using synergetic control. In addition, five cases are incorporated to evaluate error function. In addition, a brief comparative study is added to contrast the simulation results with theoretical modeling. Cancerous tumor cells divide uncontrollably, which results in either tumor or harm to the immune system of the body. Due to the destructive effects of chemotherapy, optimal medications are needed. Therefore, possible treatment methods should be controlled to maintain the constant/continuous dose for affecting the spreading of cancerous tumor cells. Rapid growth of cells is classified into primary and secondary types. In giving a proper response, the immune system plays an important role. This is considered a natural process while fighting against tumors. In recent days, achieving a better method to treat tumors is the prime focus of researchers. Mathematical modeling of tumors uses combined immune, vaccine, and chemotherapies to check performance stability. In this research paper, mathematical modeling is utilized with reference to cancerous tumor growth, the immune system, and normal cells, which are directly affected by the process of chemotherapy. This paper presents novel techniques, which include Bernstein polynomial (BSP) with genetic algorithm (GA), sliding mode controller (SMC), and synergetic control (SC), for giving a possible solution to the cancerous tumor cells (CCs) model. Through GA, random population is generated to evaluate fitness. SMC is used for the continuous exponential dose of chemotherapy to reduce CCs in about forty-five days. In addition, error function consists of five cases that include normal cells (NCs), immune cells (ICs), CCs, and chemotherapy. Furthermore, the drug control process is explained in all the cases. In simulation results, utilizing SC has completely eliminated CCs in nearly five days. The proposed approach reduces CCs as early as possible. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of computing the rank of a block-structured symbolic matrix (a generic partitioned matrix) A = (A α β x α β) , where A α β is a 2 × 2 matrix over a field F and x α β is an indeterminate for α = 1 , 2 , ⋯ , μ and β = 1 , 2 , ⋯ , ν . This problem can be viewed as an algebraic generalization of the bipartite matching problem and was considered by Iwata and Murota (SIAM J Matrix Anal Appl 16(3):719–734, 1995). Recent interests in this problem lie in the connection with non-commutative Edmonds' problem by Ivanyos et al. (Comput Complex 27:561–593, 2018) and Garg et al. (Found. Comput. Math. 20:223–290, 2020), where a result by Iwata and Murota implicitly states that the rank and non-commutative rank (nc-rank) are the same for this class of symbolic matrices. The main result of this paper is a simple and combinatorial O ((μ ν) 2 min { μ , ν }) -time algorithm for computing the symbolic rank of a (2 × 2) -type generic partitioned matrix of size 2 μ × 2 ν . Our algorithm is inspired by the Wong sequence algorithm by Ivanyos et al. for the nc-rank of a general symbolic matrix, and requires no blow-up operation, no field extension, and no additional care for bounding the bit-size. Moreover it naturally provides a maximum rank completion of A for an arbitrary field F . [ABSTRACT FROM AUTHOR]

In the paper "Why Cryptosystems Fail", Ross Anderson ponders the question about why cryptosystems really fail. Obviously, there may be weak crypto-algorithms, too short key lengths and flawed crypto-protocols. However, these were not the main reason why cryptosystems failed. Anderson discovered that the problem had more to do with misplaced trust and misconceptions of the threats the systems faced. Now, more than 25 years later, it seems prudent to revisit the question of why cryptosystems fail. We investigate the original paper, and evaluate to what extent the situation is similar today. [ABSTRACT FROM AUTHOR]

Increasingly, scholarly articles contain URI references to “web at large” resources including project web sites, scholarly wikis, ontologies, online debates, presentations, blogs, and videos. Authors reference such resources to provide essential context for the research they report on. A reader who visits a web at large resource by following a URI reference in an article, some time after its publication, is led to believe that the resource’s content is representative of what the author originally referenced. However, due to the dynamic nature of the web, that may very well not be the case. We reuse a dataset from a previous study in which several authors of this paper were involved, and investigate to what extent the textual content of web at large resources referenced in a vast collection of Science, Technology, and Medicine (STM) articles published between 1997 and 2012 has remained stable since the publication of the referencing article. We do so in a two-step approach that relies on various well-established similarity measures to compare textual content. In a first step, we use 19 web archives to find snapshots of referenced web at large resources that have textual content that is representative of the state of the resource around the time of publication of the referencing paper. We find that representative snapshots exist for about 30% of all URI references. In a second step, we compare the textual content of representative snapshots with that of their live web counterparts. We find that for over 75% of references the content has drifted away from what it was when referenced. These results raise significant concerns regarding the long term integrity of the web-based scholarly record and call for the deployment of techniques to combat these problems. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Frontiers of Computer Science & Technology is the property of Beijing Journal of Computer Engineering & Applications Journal Co Ltd. 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.)

The Internal Rate of Return (IRR) is used in economics as a popular method for project evaluation. Its major challenge, however, is to calculate all real rates. This paper presents an algorithm that can be used to calculate all return rates through introducing a heuristic approach based on several mathematical theorems. In order to better understand the different steps of the proposed algorithm, an overall description of the subject was first provided; it was then illustrated with more details through providing some examples. For the purpose of validation and accuracy of the results, the future value of the rates was also calculated at the end of each example. The results of the research showed that the new method had a relatively high efficiency to calculate all real rates. In addition, in the approach proposed in this paper, there is no need for the use of differentiation, and even recurring return rates are also identifiable. [ABSTRACT FROM AUTHOR]

Copyright of Turkish Journal of Oncology / Türk Onkoloji Dergisi is the property of KARE Publishing 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.)

Biometric recognition technology based on eye-movement dynamics has been in development for more than ten years. Different visual tasks, feature extraction and feature recognition methods are proposed to improve the performance of eye movement biometric system. However, the correct identification and verification rates, especially in long-term experiments, as well as the effects of visual tasks and eye trackers’ temporal and spatial resolution are still the foremost considerations in eye movement biometrics. With a focus on these issues, we proposed a new visual searching task for eye movement data collection and a new class of eye movement features for biometric recognition. In order to demonstrate the improvement of this visual searching task being used in eye movement biometrics, three other eye movement feature extraction methods were also tested on our eye movement datasets. Compared with the original results, all three methods yielded better results as expected. In addition, the biometric performance of these four feature extraction methods was also compared using the equal error rate (EER) and Rank-1 identification rate (Rank-1 IR), and the texture features introduced in this paper were ultimately shown to offer some advantages with regard to long-term stability and robustness over time and spatial precision. Finally, the results of different combinations of these methods with a score-level fusion method indicated that multi-biometric methods perform better in most cases. [ABSTRACT FROM AUTHOR]

With the rapid development of artificial intelligence (AI) concept technology, it promotes the innovation of educational concept. Mostly for the education information analysis in the class of mathematics in the university, it should be based on a big data-driven system to promote the quality of teaching in the classroom. In the method of teaching math in university, teachers should take full advantage of the benefits of a big data-driven system powered by AI, grow a good teaching model for students, promote education through big data, progressively teach students according to their aptitude, develop in a tailored direction, increase teaching quality and effectiveness, and finally create more great talents for our country. For the sake of improving the resource sharing and the management level of the curriculum which teaches advanced knowledge about mathematics teaching, based on a particle swarm optimization algorithm, an advanced math teaching system is proposed in this paper. The fusion model that can be used in the teaching process of math in university is constructed, the adaptive scheduling of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resources is realized by an optimization algorithm used for fusion particle swarm, the autocorrelation feature of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resources is extracted, and the adaptive optimization of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching resource fusion is realized by fuzzy correlation feature matching and statistical analysis. In the process of particle swarm optimization, the combination of statistical features is studied and managed, the resource scheduling and information fusion are realized, and the management capability of the curriculum which teaches advanced knowledge about mathematics auxiliary teaching is promoted, and the experimental results demonstrate that the designed system has a high integration of teaching information resources and strong information scheduling ability and improved the management level of the curriculum which teaches advanced knowledge about mathematics complementary teaching. [ABSTRACT FROM AUTHOR]

In the early years of school, pupils have a very positive approach towards any new topic. Very often, the first contact with mathematics in the Italian school risks giving a limited and somehow negative impression, generating long-lasting effects. In this paper, we report on a series of experiences carried out in a second-year class of a primary school that allowed us to introduce new concepts and approaches through games and puzzles. The aim was to stimulate the creativity and empower pupils. We have used simple materials and applied the Puzzle-Based Learning method. Despite the limited time devoted to this experience, the outcomes have been extremely positive. [ABSTRACT FROM AUTHOR]

There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and they can be used for the usual examples of commutative rings. To the contrary of the classical versions, the constructive versions have a clear computational content. This paper investigates the computational relationship between three possible constructive definitions of the valuative dimension of a commutative ring. In doing so, it proves these constructive versions to be equivalent within constructive mathematics. [ABSTRACT FROM AUTHOR]

In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques. [ABSTRACT FROM AUTHOR]

Background: Readability metrics provide us with an objective and efficient way to assess the quality of educational texts. We can use the readability measures for finding assessment items that are difficult to read for a given grade level. Hard‐to‐read math word problems can put some students at a disadvantage if they are behind in their literacy learning. Despite their math abilities, these students can perform poorly on difficult‐to‐read word problems because of their poor reading skills. Less readable math tests can create equity issues for students who are relatively new to the language of assessment. Less readable test items can also affect the assessment's construct validity by partially measuring reading comprehension. Objectives: This study shows how large language models help us improve the readability of math assessment items. Methods: We analysed 250 test items from grades 3 to 5 of EngageNY, an open‐source curriculum. We used the GPT‐3 AI system to simplify the text of these math word problems. We used text prompts and the few‐shot learning method for the simplification task. Results and Conclusions: On average, GPT‐3 AI produced output passages that showed improvements in readability metrics, but the outputs had a large amount of noise and were often unrelated to the input. We used thresholds over text similarity metrics and changes in readability measures to filter out the noise. We found meaningful simplifications that can be given to item authors as suggestions for improvement. Takeaways: GPT‐3 AI is capable of simplifying hard‐to‐read math word problems. The model generates noisy simplifications using text prompts or few‐shot learning methods. The noise can be filtered using text similarity and readability measures. The meaningful simplifications AI produces are sound but not ready to be used as a direct replacement for the original items. To improve test quality, simplifications can be suggested to item authors at the time of digital question authoring. Lay Description: What is Known About the Subject: Difficult to read math assessment items cause measurement and equity issuesReadability of math word problems negatively correlated with outcomes What Our Paper Adds: GPT‐3 AI system is capable to simplify math word problemsPrompt‐based and few‐shot learning‐based approaches are able to create meaningful simplifications, but with a very low accuracy rateText similarity and readability measures can be used to filter out noisy outputs and discover interesting simplifications What are the Implications for Practitioners: GPT‐3 AI is capable of generating relevant math world problem simplificationsSimplified text can be used as suggestions to question authors during the digital item authoring process [ABSTRACT FROM AUTHOR]

Let a,b ∈ Rn be column vectors, and (u, v) be the inner product of vectors u and v on Rn. Let G ⊂ GL(n,R) be a compact matrix group. For A ∈ G and a continue function f on G, the integral ∫G f (A)dA is the invariant integral of the compact group G. In this paper, we study the inequality ∀x ∈ Rn ∫G e(Aa, x)dA ≥ ∫G e(Ab, x)dA. We prove that the above inequality holds if and only if b ∈Conv(Ga) . This work follows a series of results, that is, Muirhead (1903), Hardy, Littlewood and P`olya (1932), Rado (1952), Daykin (1971), Kimelfeld (1995) and Schulman (2009). Furthermore, We construct an determining algorithm when G is finite. Compared with other effective algorithms, this one is symbolic and easy to implement on computer. [ABSTRACT FROM AUTHOR]

In this paper, fast numerical methods for solving the real quasi-symmetric Toeplitz linear system are studied in two stages. First, based on an order-reduction algorithm and the factorization of Toeplitz matrix inversion, a sequence of linear systems with a constant symmetric Toeplitz matrix are solved. Second, two new fast algorithms are employed to solve the real quasi-symmetric Toeplitz linear system. Furthermore, we show a fast algorithm for quasi-symmetric Toeplitz matrix-vector multiplication. In addition, the stability analysis of the splitting symmetric Toeplitz inversion is discussed. In mathematical or engineering problems, the proposed algorithms are extraordinarily effective for solving a sequence of linear systems with a constant symmetric Toeplitz matrix. Fast matrix-vector multiplication and a quasi-symmetric Toeplitz linear solver are proven to be suitable for image encryption and decryption. [ABSTRACT FROM AUTHOR]

Mixed models: Models allowing for continuous heterogeneity by assuming that value of one or more parameters follow a specified distribution have become increasingly popular. This is known as ‘mixing’ parameters, and it is standard practice by researchers - and the default option in many statistical programs - to base test statistics for mixed models on simulations using asymmetric draws (e.g. Halton draws). Problem 1: Inconsistent LR tests due to asymmetric draws:: This paper shows that when the estimated likelihood functions depend on standard deviations of mixed parameters this practice is very likely to cause misleading test results for the number of draws usually used today. The paper illustrates that increasing the number of draws is a very inefficient solution strategy requiring very large numbers of draws to ensure against misleading test statistics. The main conclusion of this paper is that the problem can be solved completely by using fully antithetic draws, and that using one dimensionally antithetic draws is not enough to solve the problem. Problem 2: Maintaining the correct dimensions when reducing the mixing distribution:: A second point of the paper is that even when fully antithetic draws are used, models reducing the dimension of the mixing distribution must replicate the relevant dimensions of the quasi-random draws in the simulation of the restricted likelihood. Again this is not standard in research or statistical programs. The paper therefore recommends using fully antithetic draws replicating the relevant dimensions of the quasi-random draws in the simulation of the restricted likelihood and that this should become the default option in statistical programs. JEL classification: C15; C25. [ABSTRACT FROM AUTHOR]