22 papers · ranked by Valyu relevance
S. C. Shen, Peijun Shen, Danhao Zhu
This paper presents RevOrder, a novel technique aimed at improving arithmetic operations in large language models (LLMs) by reversing the output digits in addition, subtraction, and n-digit by 1-digit (nD by 1D) multiplication tasks. Our method significantly reduces the Count of Sequential Intermediate Digits (CSID) to…
Dawei Liu, Xin Tan, Huifen Yan, Wei Li + 1 more
Skillful utilization of mental arithmetic can significantly improve students’ mathematical computation ability. However, it was observed that primary school students often resort to reiterating the process of written arithmetic in their minds during mental arithmetic, which is not conducive to their numerical ability…
Shufang Chen, Dawei Liu, Huifen Yan, Yong Ma
Introduction Arithmetic calculation is a fundamental skill for mathematical learning and daily life. However, elementary school students often make errors in practice. Methods Grounded in the schema theory and the memory retrieval theory of mental arithmetic, this study employs a controlled experiment to investigate…
Daichi Mukunoki, Katsuhisa Ozaki
—To obtain accurate results in numerical computation, high-precision arithmetic is a straightforward approach. However, most processors lack hardware support for floatingpoint formats beyond double precision (FP64). Double-word arithmetic (Dekker 1971) extends precision by using standard floating-point operations to…
Elisabeth Goettfried, Laura Zamarian, Jerrell Cassady
The investigation of eye movements has been shown to provide valuable insights into a variety of cognitive processes. A limited number of recent studies have adopted eye-tracking to investigate the processes underlying simple and complex arithmetic. Here, we review and discuss these studies. We identify two lines of…
Trond Steihaug
The Fibonacci numbers are familiar to all of us. They appear unexpectedly often in mathematics, so much there is an entire journal and a sequence of conferences dedicated to their study. However, there is also another sequence of numbers associated with Fibonacci. In The On-Line Encyclopedia of Integer Sequences, a…
Nuh Aydin, Mohammad K. Azarian, Omid Khormali, Ghaya Mtimet
The square-and-multiply algorithm, also known as binary exponentiation or repeated squaring, is a technique for fast exponentiation commonly used in modern cryptography and computational number theory. Despite its prominence, the historical origins of the algorithm are not known with certainty. This paper critically…
Percy K Mistry, Hyesang Chang, Dawlat El-Said, Vinod Menon
Children exhibit remarkable variability in their mathematical problem-solving abilities, yet the cognitive, metacognitive and affective mechanisms underlying these individual differences remain poorly understood. We developed a novel Bayesian model of arithmetic problem-solving (BMAPS) to uncover the latent processes…
Pagdame Tiebekabe, K. R. Kakanou, Hamid Ben Yakkou
The concept of Narayana's cows numbers, derived from Indian mythology and Hinduism, holds a significant place in mathematics. These numbers have been extensively studied due to their properties and relationships with other mathematical sequences, and their important applications in other various fields such as…
Bing H. Ngu, Huy P. Phan, Jérôme Prado
Central to cognitive load theory is the concept of element interactivity, which reflects the complexity of material. The complexity of linear equations depends on the number of operational and relational lines and the nature of the operation (balance versus inverse) in the solution procedure. A relational line refers…
Amal Altamimi, Belgacem Ben Youssef
The square root operation is indispensable in a myriad of computational science and engineering applications. Various computational techniques have been devised to approximate its value. In particular, convergence methods employed in this regard are highly affected by the initial approximation of the seed value.…
Alexandre Zénon, Samuel Salvaggio, Michael Andres
The assumption that the brain relies on Bayesian inference has been successful in accounting for many behavioural and neurophysiological observations, but to date, dependence on such mechanism has not been assessed in the context of arithmetic. Bayesian inference implies the representation of uncertainty and reliance…
Tomoya Nakai, Jérôme Prado
The ability to learn simple arithmetic is often thought to rely on the associative nature of human memory, where repeated exposure to arithmetic problems strengthens the relations between operands and outcomes. This view is reminiscent of learning in large language artificial neural networks (ANNs), where training…
Serena Dattola, Lilla Bonanno, Augusto Ielo, Angelica Quercia + 4 more
'Angelo Quartarone' 'Fabio La Foresta' 'Dante Mantini' 'Larbi Boubchir'] The neural underpinnings of mental calculation, the fundamentals of arithmetic representations and processes, and the development of arithmetic abilities have been explored by researchers over the years. In the present work, we report a study that…
Manqi Zhou, Shiyan Ji, Yalun Zhang, Huijuan Shen + 9 more
Mastering basic arithmetic lays the foundation for lifelong mathematical achievement, yet how the neural mechanisms underlying addition and subtraction calculations develop during childhood remain unclear. This study investigated the developmental trajectories of addition and subtraction calculations in school-aged…
Pedro Pinheiro-Chagas, Clara Sava-Segal, Serdar Akkol, Amy Daitch + 1 more
Previous neuroimaging studies have offered unique insights about the spatial organization of activations and deactivations across the brain, however these were not powered to explore the exact timing of events at the subsecond scale combined with precise anatomical source information at the level of individual brains.…
Zhihao Lan, WanZhen Liang
The variational quantum eigensolver (VQE) algorithm can simulate the chemical systems such as molecules in the noisy intermediate-scale quantum devices and shows promising applications in quantum chemistry simulations. The accuracy and computational cost of the VQE simulations are determined by the underlying Ansätze.…
Fairouz Kamareddine, Jonathan P. Seldin
This paper looks at how ancient mathematicians (and especially the Pythagorean school) were faced by problems/paradoxes associated with the infinite which led them to juggle two systems of numbers: the discrete whole/rationals which were handled arithmetically and the continuous magnitude quantities which were handled…
Osvaldo Skliar, Sherry Gapper, Ricardo E. Monge
A description is provided of how the Square Wave Method (SWM) can be applied to analyze sequences of bases of human DNA. The results obtained are displayed using the Square Wave Transform (SWT), an SWM tool. It is hypothesized that the results of this analysis can be of interest, in certain cases, to understand the…
Yingqi Tian, Zhaoxuan Xie, Zhen Luo, Haibo Ma
Using the mixed precision strategy to optimize quantum chemistry codes has been proved promising in saving computational cost and maintaining chemical accuracy. Here, an efficient mixed-precision density matrix renormalization group (DMRG) scheme, containing a two-level mixed-precision hierarchy, is developed and…
V. N. Krishnachandran
astronomy and mathematics Authors: ['V. N. Krishnachandran'] | 1 | Introduction | | 3 | | --- | --- | --- | --- | | 2 | ¯ | Bhaskara I's approximation to the sine function | 4 | | | 2.1 | The approximation formula | 4 | | | 2.2 | Rendering in modern notations | 5 | | | 2.3 | Accuracy of the formula | 6 | | | 2.4 | On…
Authors not listed
While the method of manual inspection reliably produces correct results at the introductory level, it can often appear untidy and unintuitive and lacks teachable depth. This paper presents a novel alternative approach designed to achieve the same outcomes as manual inspection but with enhanced clarity. It serves as…