Hasil untuk "Mathematics"

Pan Lu, Hritik Bansal, Tony Xia et al.

Large Language Models (LLMs) and Large Multimodal Models (LMMs) exhibit impressive problem-solving skills in many tasks and domains, but their ability in mathematical reasoning in visual contexts has not been systematically studied. To bridge this gap, we present MathVista, a benchmark designed to combine challenges from diverse mathematical and visual tasks. It consists of 6,141 examples, derived from 28 existing multimodal datasets involving mathematics and 3 newly created datasets (i.e., IQTest, FunctionQA, and PaperQA). Completing these tasks requires fine-grained, deep visual understanding and compositional reasoning, which all state-of-the-art foundation models find challenging. With MathVista, we have conducted a comprehensive, quantitative evaluation of 12 prominent foundation models. The best-performing GPT-4V model achieves an overall accuracy of 49.9%, substantially outperforming Bard, the second-best performer, by 15.1%. Our in-depth analysis reveals that the superiority of GPT-4V is mainly attributed to its enhanced visual perception and mathematical reasoning. However, GPT-4V still falls short of human performance by 10.4%, as it often struggles to understand complex figures and perform rigorous reasoning. This significant gap underscores the critical role that MathVista will play in the development of general-purpose AI agents capable of tackling mathematically intensive and visually rich real-world tasks. We further explore the new ability of self-verification, the application of self-consistency, and the interactive chatbot capabilities of GPT-4V, highlighting its promising potential for future research. The project is available at https://mathvista.github.io/.

R. Goodstein, L. Wittgenstein, R. Rhees et al.

S. S. Stevens

J. Bezdek

U. Merzbach, C. Boyer

David Pimm

W. Blum, Mogens Niss

D. Mumford, Jatin Shah

P. Wilmott, S. Howison, J. Dewynne

Bryant Candra Wijaya, Fanny Rahma Eka Aprianny, Amelia Putri Wahyuni et al.

This study explores geometric concepts embedded in the ornaments of Tegowangi Temple through an ethnomathematical perspective. Previous studies on temple-based ethnomathematics have primarily focused on general geometric forms, with limited attention to specific concepts and their pedagogical relevance, particularly in the context of Tegowangi Temple. Addressing this gap, this research aims to identify and analyse the concepts of reflection, similarity, and circles within the temple’s ornamental structures. A qualitative exploratory design with an ethnographic approach was employed. Data were collected through observation, interviews, and documentation, and analysed using domain and taxonomic analysis to interpret mathematical representations within cultural artefacts. The findings reveal that reflection is evident in the symmetrical structure of corner kala ornaments, in the similarity of the yoni's proportional dimensions, and in circular concepts in the decorative patterns of the Perwara Temple. These concepts were derived through systematic visual and structural analysis of ornament forms. Conceptually, the study contributes to a deeper understanding of geometry in cultural contexts, while pedagogically, it provides contextual learning resources for junior high school mathematics

Ermelinda Gjeta, Diellëza Lajçi, Avni Hajdari et al.

Populations of Anthyllis vulneraria ssp. vulneraria and A. vulneraria ssp. vallesiaca are found in close vicinity in Val Piora, where the geological situation changes abruptly between basic and acidic substrates. At three sites with populations of A. vulneraria s. lato, one in basic soil, one in acidic soil, and one in a mixed area, three samples of a total of sixty plants were collected, and flower morphology and physiological activity was determined. Of each population, the number of plants using Braun-Blanquet squares was determined. The frequency and indication values showed that the two subspecies are adapted to different pH values. A. v. ssp. vallesiaca and A. v. ssp. vulneraria are clearly well separated by the red striped keel, the flag dimension, and flower size. In areas where the two species overlap, introgression occurs. The hybrid population consisted of yellow hybrid plants with red keel, yellow plants, and white plants with a red keel. The hybrids are present at a pH value between the ones of the two subspecies. The rapid increase in chlorophyll fluorescence also clearly showed that the two subspecies differed in their kinetics. The values of the hybrid plants (yellow with red keel) were between those of the populations of the two subspecies.

Dimitri Dine

We study the relationship between almost mathematics, condensed mathematics and the categories of seminormed and Banach modules over a Banach ring $A$, with submetric (norm-decreasing) $A$-module homomorphisms for morphisms. If $A$ is a Banach ring with a norm-multiplicative topologically nilpotent unit $\varpi$ contained in the closed unit ball $A_{\leq1}$ such that $\varpi$ admits a compatible system of $p$-power roots $\varpi^{1/p^{n}}$ with \begin{equation*}\lVert\varpi^{1/p^{n}}\rVert=\lVert\varpi\rVert^{1/p^{n}}\end{equation*}for all $n$, we prove that the "almost closed unit ball" functor \begin{equation*}M\mapsto M_{\leq1}^{a}\end{equation*}is an equivalence between the category of Banach $A$-modules and submetric $A$-module maps and the category of $\varpi$-adically complete, $\varpi$-torsion-free almost $(A_{\leq1}, (\varpi^{1/p^{\infty}}))$-modules. We also obtain an analogous result for Banach algebras and almost algebras. The main novelty in our approach is that we show that the norm on the Banach module $M$ is completely determined by the corresponding almost $A_{\leq1}$-module $M_{\leq1}^{a}$, rather than being determined only up to equivalence. We deduce from our results the existence of a natural fully faithful embedding of the category of Banach $A$-modules and submetric $A$-module maps into the category of (static) condensed almost $(A_{\leq1}, (\varpi^{1/p^{\infty}}))$-modules in the sense of Mann, which factors through the full subcategory of solid condensed $(A_{\leq1}, (\varpi^{1/p^{\infty}}))$-almost modules. If $A$ is perfectoid and the adic spectrum of $(A, A^{\circ})$ is totally disconnected, we show that this embedding transforms the complete tensor product of Banach $A$-modules into (an almost analog of) the solid tensor product of solid condensed almost modules.

Aslanbek Naziev, Irina Zemlyakova

The paper examines the construction of a course in mathematical analysis at a pedagogical university, aimed at developing the ability of future mathematics teachers to detect and solve problems related to finding proofs. Key words: teaching mathematics, teacher training, discovery of proofs, quantifiers, mathematical analysis

I. Goodman, R. Mahler, H. Nguyen

Komarudin Komarudin, Suherman Suherman, Laila Puspita

This study aims to assess the feasibility, teacher and student responses, and effectiveness of the STEM-based digital pocketbook on the topic of Systems of Linear Equations in Two Variables (SPLDV). The subjects of this research were junior high school students in Bandar Lampung. Data collection instruments included questionnaires distributed to subject matter experts, media experts, and student respondents. The method in this research uses the ADDIE model which consists of 5 stages, namely: Analysis, design, development, implementation, and evaluation. The findings indicate that the developed learning media are highly suitable and engaging for mathematics instruction, particularly concerning SPLDV topics. However, due to the global COVID-19 pandemic, the research did not progress to the implementation phase, thereby precluding the effectiveness testing of the STEM-based digital pocketbook

Xianwei ZHU, Wei LIU, Zihao LIU et al.

To address the difficulty faced by network security operation and maintenance personnel in timely and accurate identification of required data during network security event analysis, a recommendation algorithm based on a knowledge graph for network security events was proposed.The algorithm utilized the network threat framework ATT＆amp;CK to construct an ontology model and establish a network threat knowledge graph based on this model.It extracted relevant security data such as attack techniques, vulnerabilities, and defense measures into interconnected security knowledge within the knowledge graph.Entity data was extracted based on the knowledge graph, and entity vectors were obtained using the TransH algorithm.These entity vectors were then used to calculate data similarity between entities in network threat data.Disposal behaviors were extracted from literature on network security event handling and treated as network security data entities.A disposal behavior matrix was constructed, and the behavior matrix enabled the vector representation of network threat data.The similarity of network threat data entities was calculated based on disposal behaviors.Finally, the similarity between network threat data and threat data under network security event handling behavior was fused to generate a data recommendation list for network security events, which established correlations between network threat domains based on user behavior.Experimental results demonstrate that the algorithm performs optimally when the fusion weight α=7 and the recommended data volume K=5, achieving a recall rate of 62.37% and an accuracy rate of 68.23%.By incorporating disposition behavior similarity in addition to data similarity, the algorithm better represents factual disposition behavior.Compared to other algorithms, this algorithm exhibits significant advantages in recall rate and accuracy, particularly when the recommended data volume is less than 10.

Sathya P, Gnanasekaran P

Crop yield forecasting has been well studied in recent decades and is significant in protecting food security. Crop growth is a complex phenomenon that depends on various factors. Machine learning and deep learning trends have emerged as important innovations in this field. We propose to utilize crop, weather, and soil data from agricultural datasets to evaluate yield prediction behavior. Paddy being a staple food crop in India is chosen for this research. In this paper, we propose hybrid architecture for paddy yield prediction, namely, MLR-LSTM, which combines Multiple Linear Regression and Long Short-Term Memory to utilize their complementary nature. The results are compared with traditional machine learning methods such as Support vector machine, Long short-term memory and Random forest method. Evaluation metrics such as Coefficient of Determination (R2), Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Mean Square Error (MSE), F1 score, Recall, and Precision are used to evaluate the hybrid method and traditional models. The results obtained from the proposed hybrid method indicates that the hybrid model delivers better R2, RMSE, MAE, MSE values of 0.93, 0.1549, 0.199, and 0.024 respectively.

Jingying Gao, Qingmei Bai, Siriguleng He et al.

The paper introduces a new two-level time-mesh difference scheme for solving the symmetric regularized long wave equation. The scheme consists of three steps. A coarse time-mesh and a fine time-mesh are defined, and the equation is solved using an existing nonlinear scheme on the coarse time-mesh. Lagrange’s linear interpolation formula is employed to obtain all preliminary solutions on the fine time-mesh. Based on the preliminary solutions, Taylor’s formula is utilized to construct a linear system for the equation on the fine time-mesh. The convergence and stability of the scheme is analyzed, providing the convergence rates of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msubsup><mi>τ</mi><mi>F</mi><mn>2</mn></msubsup><mo>+</mo><msubsup><mi>τ</mi><mi>C</mi><mn>4</mn></msubsup><mo>+</mo><msup><mi>h</mi><mn>4</mn></msup><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> in the discrete <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mo>∞</mo></msub></semantics></math></inline-formula>-norm for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>u</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula> and in the discrete <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>L</mi><mn>2</mn></msub></semantics></math></inline-formula>-norm for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>ρ</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></semantics></math></inline-formula>. Numerical simulation results show that the proposed scheme achieves equivalent error levels and convergence rates to the nonlinear scheme, while also reducing CPU time by over half, which indicates that the new method is more efficient. Furthermore, compared to the earlier time two-mesh method developed by the authors, the proposed scheme significantly reduces the error between the numerical and exact solutions, which means that the proposed scheme is more accurate. Additionally, the effectiveness of the new scheme is discussed in terms of the corresponding conservation laws and long-time simulations.

Binayak Panda, Sudhanshu Shekhar Bisoyi, Sidhanta Panigrahy

Dependence on the internet and computer programs demonstrates the significance of computer programs in our day-to-day lives. Such demands motivate malware developers to create more malware, both in terms of quantity and variety. Researchers are constantly faced with hurdles while attempting to protect themselves from potential hazards and risks due to malware authors’ usage of code obfuscation techniques. Metamorphic and polymorphic variations are easily able to elude the widely utilized signature-based detection procedures. Researchers are more interested in deep learning approaches than machine learning techniques to analyze the behavior of such a vast number of virus variants. Researchers have been drawn to the categorization of malware within itself in addition to the classification of malware against benign programs to examine the behavioral differences between them. In order to investigate the relationship between the application programming interface (API) calls throughout API sequences and classify them, this work uses the one-dimensional convolutional neural network (1D-CNN) model to solve a multiclass classification problem. On API sequences, feature vectors for distinctive APIs are created using the Word2Vec word embedding approach and the skip-gram model. The one-vs.-rest approach is used to train 1D-CNN models to categorize malware, and all of them are then combined with a suggested ModifiedSoftVoting algorithm to improve classification. On the open benchmark dataset Mal-API-2019, the suggested ensembled 1D-CNN architecture captures improved evaluation scores with an accuracy of 0.90, a weighted average F1-score of 0.90, and an AUC score of more than 0.96 for all classes of malware.

M. Muñoz Pérez

Putnam and Finkelstein can be read as providing an answer to Kripke's skeptical argument by appealing to the way mathematics is commonly pursued. Nowadays, the debate surrounding pluralism has questioned the postulation of a unique way of developing mathematical activity. In this paper, we wish to reformulate Kripke's argument as a challenge for the conjunction of 'ifthenism' and a reasonable form of pluralism (which we have called '$V$-pluralism') and, at the same time, propose a reading of some passages of the 'Philosophical Investigations' as a solution. Our conclusion is that, in order for pluralism to be preserved, we need to clarify both the fact that we make definite 'decisions' and the philosophical value that they, as we argue, bear. To investigate the nature of this value is one of the further tasks want to cover in this article.