An important feature of modern science and engineering is that data of various kinds is being produced at an unprecedented rate. This is so in part because of new experimental methods, and in part because of the increase in the availability of high powered computing technology. It is also clear that the nature of the data we are obtaining is significantly different. For example, it is now often the case that we are given data in the form of very long vectors, where all but a few of the coordinates turn out to be irrelevant to the questions of interest, and further that we don’t necessarily know which coordinates are the interesting ones. A related fact is that the data is often very high-dimensional, which severely restricts our ability to visualize it. The data obtained is also often much noisier than in the past and has more missing information (missing data). This is particularly so in the case of biological data, particularly high throughput data from microarray or other sources. Our ability to analyze this data, both in terms of quantity and the nature of the data, is clearly not keeping pace with the data being produced. In this paper, we will discuss how geometry and topology can be applied to make useful contributions to the analysis of various kinds of data. Geometry and topology are very natural tools to apply in this direction, since geometry can be regarded as the study of distance functions, and what one often works with are distance functions on large finite sets of data. The mathematical formalism which has been developed for incorporating geometric and topological techniques deals with point clouds, i.e. finite sets of points equipped with a distance function. It then adapts tools from the various branches of geometry to the study of point clouds. The point clouds are intended to be thought of as finite samples taken from a geometric object, perhaps with noise. Here are some of the key points which come up when applying these geometric methods to data analysis. • Qualitative information is needed: One important goal of data analysis is to allow the user to obtain knowledge about the data, i.e. to understand how it is organized on a large scale. For example, if we imagine that we are looking at a data set constructed somehow from diabetes patients, it would be important to develop the understanding that there are two types of the disease, namely the juvenile and adult onset forms. Once that is established, one of course wants to develop quantitative methods for distinguishing them, but the first insight about the distinct forms of the disease is key.
This research analyzes the marine route plan from Shanghai to Vladivostok utilizing Dijkstra’s algorithm, Markov chain analysis, game theory, and congestion analysis. Dijkstra determines the route through Busan and Hungnam as the shortest, with a total distance of 2114 kilometers and minimal travel time. The Markov chain analysis supported the designated path by demonstrating greater transition probabilities compared to other routes, so establishing it as the most probable option. Experts in game theory, particularly on the Nash equilibrium, demonstrated that cooperation significantly reduced operating expenses. Further congestion research corroborated that the Shanghai-Busan-Hungnam-Vladivostok route offers a cost advantage, and even with the inclusion of congestion, the route remains less expensive. The study collectively advocates for the consideration of distance, likelihood, collaboration, and congestion while selecting the optimal maritime route, hence enhancing efficiency in maritime logistics.
Deni Andika Nur pratama, Wahyu Lestari, Darwin Djeni
This study aims to examine the effect of the application of ICT learning media based on Wordwall and QuizWhizzer, on students' interest in learning mathematics.The method in this study is quantitative applying a correlation approach with a sample of 38 students of class VIII MTs SA Tarbiyatus Shibyan. Data were collected through observation, questi onnaires, interviews, documentation, and analyzed by applying the Pearson Product Moment multiple correlation test (Correlation Multiple). The results of the study showed that Wordwall has a very strong relationship with students' interest in learning while QuizWhizzer showed a strong relationship . When both media were used simultaneously, the results of the multiple correlation test showed a very strong relationship with an result of and a coefficient of determination , which means the variation in students' interest in learning can be described by the application of Wordwall and QuizWhizzer. Thus, the application of these two media simultaneously has proven effective in optimizing students' interest in learning. Therefore, educators are advised to integrate Wordwall and QuizWhizzer into their learning to develop a more inspiring and responsive learning experience.
Keyword: Information and Communication Technology (ICT) Learning Media Wordwall, QuizWhizzwer, Learning Interest.
We propose a novel two-stage framework to detect lead-lag relationships in the Chinese A-share market. First, long-term coupling between stocks is measured via daily data using correlation, dynamic time warping, and rank-based metrics. Then, high-frequency data (1-, 5-, and 15-minute) is used to detect statistically significant lead-lag patterns via cross-correlation, Granger causality, and regression models. Our low-coupling modular system supports scalable data processing and improves reproducibility. Results show that strongly coupled stock pairs often exhibit lead-lag effects, especially at finer time scales. These findings provide insights into market microstructure and quantitative trading opportunities.
With the continuous development of artificial intelligence technology, using machine learning technology to predict market trends may no longer be out of reach. In recent years, artificial intelligence has become a research hotspot in the academic circle,and it has been widely used in image recognition, natural language processing and other fields, and also has a huge impact on the field of quantitative investment. As an investment method to obtain stable returns through data analysis, model construction and program trading, quantitative investment is deeply loved by financial institutions and investors. At the same time, as an important application field of quantitative investment, the quantitative investment strategy based on artificial intelligence technology arises at the historic moment.How to apply artificial intelligence to quantitative investment, so as to better achieve profit and risk control, has also become the focus and difficulty of the research. From a global perspective, inflation in the US and the Federal Reserve are the concerns of investors, which to some extent affects the direction of global assets, including the Chinese stock market. This paper studies the application of AI technology, quantitative investment, and AI technology in quantitative investment, aiming to provide investors with auxiliary decision-making, reduce the difficulty of investment analysis, and help them to obtain higher returns.
Jikai Wang, Abdolnaser Ghazagh, Sonam Smitha Ravi
et al.
A standardized phase retrieval algorithm is presented and applied to an industry-grade high-energy ultrashort pulsed laser to uncover its spatial phase distribution. We describe in detail how to modify the well-known algorithm in order to characterize particularly strong light sources from intensity measurements only. With complete information about the optical field of the unknown light source at hand, virtual back propagation can reveal weak points in the light path such as apertures or damaged components.
Yui Hayashi, Shun Katakami, Shigeo Kuwamoto
et al.
Small-angle scattering (SAS) is a key experimental technique for analyzing nano-scale structures in various materials.In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting.This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models.We assess the performance of our method through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that our proposed method analysis approach yields highly accurate and interpretable results.We also discuss the ability of our method to analyze a range of mixing ratios and particle size ratios for mixed components, along with its precision in model evaluation by the degree of fitting.Our proposed method effectively facilitates quantitative analysis of nano-scale sample structures in SAS, which has traditionally been challenging, and is expected to significantly contribute to advancements in a wide range of fields.
Total fractional-order variation (TFOV) in image deblurring problems can reduce/remove the staircase problems observed with the image deblurring technique by using the standard total variation (TV) model. However, the discretization of the Euler–Lagrange equations associated with the TFOV model generates a saddle point system of equations where the coefficient matrix of this system is dense and ill conditioned (it has a huge condition number). The ill-conditioned property leads to slowing of the convergence of any iterative method, such as Krylov subspace methods. One treatment for the slowness property is to apply the preconditioning technique. In this paper, we propose a block triangular preconditioner because we know that using the exact triangular preconditioner leads to a preconditioned matrix with exactly two distinct eigenvalues. This means that we need at most two iterations to converge to the exact solution. However, we cannot use the exact preconditioner because the Shur complement of our system is of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mo>=</mo><msup><mi>K</mi><mo>*</mo></msup><mi>K</mi><mo>+</mo><mi>λ</mi><msub><mi>L</mi><mi>α</mi></msub></mrow></semantics></math></inline-formula> which is a huge and dense matrix. The first matrix, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><msup><mrow></mrow><mo>*</mo></msup><mi>K</mi></mrow></semantics></math></inline-formula>, comes from the blurred operator, while the second one is from the TFOV regularization model. To overcome this difficulty, we propose two preconditioners based on the circulant and standard TV matrices. In our algorithm, we use the flexible preconditioned GMRES method for the outer iterations, the preconditioned conjugate gradient (PCG) method for the inner iterations, and the fixed point iteration (FPI) method to handle the nonlinearity. Fast convergence was found in the numerical results by using the proposed preconditioners.
Tadeusz Antczak, Manuel Arana-Jimenéz, Savin Treanţă
In this paper, we consider the class of nondifferentiable multiobjective fractional variational control problems involving the nondifferentiable terms in the numerators and in the denominators. Under univexity and generalized univexity hypotheses, we prove optimality conditions and various duality results for such nondifferentiable multiobjective fractional variational control problems. The results established in the paper generalize many similar results established earlier in the literature for such nondifferentiable multiobjective fractional variational control problems.
Aritra Dutta, El Houcine Bergou, Yunming Xiao
et al.
Optimization acceleration techniques such as momentum play a key role in state-of-the-art machine learning algorithms. Recently, generic vector sequence extrapolation techniques, such as regularized nonlinear acceleration (RNA) of Scieur et al. [22], were proposed and shown to accelerate fixed point iterations. In contrast to RNA which computes extrapolation coefficients by (approximately) setting the gradient of the objective function to zero at the extrapolated point, we propose a more direct approach, which we call direct nonlinear acceleration (DNA). In DNA, we aim to minimize (an approximation of) the function value at the extrapolated point instead. We adopt a regularized approach with regularizers designed to prevent the model from entering a region in which the functional approximation is less precise. While the computational cost of DNA is comparable to that of RNA, our direct approach significantly outperforms RNA on both synthetic and real-world datasets. While the focus of this paper is on convex problems, we obtain very encouraging results in accelerating the training of neural networks.
In this paper, we establish weak and strong convergence theorems of a two-step modified projection-type Ishikawa iterative scheme to the fixed point of α-hemicontractive mappings without any compactness assumption on the operator or the space. Our results extend, improve and generalize several previously known results of the existing literature.
Shakaiba Shafiq, Sadaf Khan, Waleed Marzouk
et al.
In this paper, a new discrete distribution called Binomial–Natural Discrete Lindley distribution is proposed by compounding the binomial and natural discrete Lindley distributions. Some properties of the distribution are discussed including the moment-generating function, moments and hazard rate function. Estimation of the distribution’s parameter is studied by methods of moments, proportions and maximum likelihood. A simulation study is performed to compare the performance of the different estimates in terms of bias and mean square error. SO<sub>2</sub> data applications are also presented to see that the new distribution is useful in modeling data.
Accurate prediction of RNA three-dimensional (3D) structure remains an unsolved challenge. Determining RNA 3D structures is crucial for understanding their functions and informing RNA-targeting drug development and synthetic biology design. The structural flexibility of RNA, which leads to scarcity of experimentally determined data, complicates computational prediction efforts. Here, we present RhoFold+, an RNA language model-based deep learning method that accurately predicts 3D structures of single-chain RNAs from sequences. By integrating an RNA language model pre-trained on ~23.7 million RNA sequences and leveraging techniques to address data scarcity, RhoFold+ offers a fully automated end-to-end pipeline for RNA 3D structure prediction. Retrospective evaluations on RNA-Puzzles and CASP15 natural RNA targets demonstrate RhoFold+'s superiority over existing methods, including human expert groups. Its efficacy and generalizability are further validated through cross-family and cross-type assessments, as well as time-censored benchmarks. Additionally, RhoFold+ predicts RNA secondary structures and inter-helical angles, providing empirically verifiable features that broaden its applicability to RNA structure and function studies.
Explicit time integration schemes coupled with Galerkin discretizations of time-dependent partial differential equations require solving a linear system with the mass matrix at each time step. For applications in structural dynamics, the solution of the linear system is frequently approximated through so-called mass lumping, which consists in replacing the mass matrix by some diagonal approximation. Mass lumping has been widely used in engineering practice for decades already and has a sound mathematical theory supporting it for finite element methods using the classical Lagrange basis. However, the theory for more general basis functions is still missing. Our paper partly addresses this shortcoming. Some special and practically relevant properties of lumped mass matrices are proved and we discuss how these properties naturally extend to banded and Kronecker product matrices whose structure allows to solve linear systems very efficiently. Our theoretical results are applied to isogeometric discretizations but are not restricted to them.
O. Pible, François Allain, Virginie Jouffret
et al.
There is an important need for the development of fast and robust methods to quantify the diversity and temporal dynamics of microbial communities in complex environmental samples. Because tandem mass spectrometry allows rapid inspection of protein content, metaproteomics is increasingly used for the phenotypic analysis of microbiota across many fields, including biotechnology, environmental ecology, and medicine. Here, we present a new method for identifying the biomass contribution of any given organism based on a signature describing the number of peptide sequences shared with all other organisms, calculated by mathematical modeling and phylogenetic relationships. This so-called “phylopeptidomics” principle allows for the calculation of the relative ratios of peptide-specified taxa by the linear combination of such signatures applied to an experimental metaproteomic dataset. We illustrate its efficiency using artificial mixtures of two closely related pathogens of clinical interest, and with more complex microbiota models. This approach paves the way to a new vision of taxonomic changes and accurate label-free quantitative metaproteomics for fine-tuned functional characterization. AZqEX-w-2DoMcPFXCsnk2V Video abstract Video abstract
This research was conducted with the aim of describing metacognitive skills with students' mathematical generalization abilities in problem solving. This type of research is a qualitative descriptive research. This research was conducted on 9th grade students by taking 5 students as research subjects. Data collection techniques used in this research were tests, interviews, and questionnaires. The results of this research indicate that students are able to apply the designs that they will use to solve problems. Even though the evaluation indicators only review the results obtained.
This chapter provides an overview of the different Artificial Intelligence (AI) systems that are being used in contemporary digital tools for Mathematics Education (ME). It is aimed at researchers in AI and Machine Learning (ML), for whom we shed some light on the specific technologies that are being used in educational applications; and at researchers in ME, for whom we clarify: i) what the possibilities of the current AI technologies are, ii) what is still out of reach and iii) what is to be expected in the near future. We start our analysis by establishing a high-level taxonomy of AI tools that are found as components in digital ME applications. Then, we describe in detail how these AI tools, and in particular ML, are being used in two key applications, specifically AI-based calculators and intelligent tutoring systems. We finish the chapter with a discussion about student modeling systems and their relationship to artificial general intelligence.
We introduce a diffuse interface box method (DIBM) for the numerical approximation on complex geometries of elliptic problems with Dirichlet boundary conditions. We derive a priori $H^1$ and $L^2$ error estimates highlighting the rôle of the mesh discretization parameter and of the diffuse interface width. Finally, we present a numerical result assessing the theoretical findings.